/sqt/ - Stupid Questions Thread - Shitty Bait Edition

homie there's already one here
>>8887234

>>8888670
>posted before the bump limit

is sexuality a spectrum?

>>8888874
no. calling it a "spectrum" implies there's a linear range of values. sexuality is more complicated than that.

/sci/ is one slow board

Why won't math get me money?

>>8888893
it will, if you use it for programming or engineering or something

What's the most rigorous linear algebra textbook?

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Can someone explain to me what's going on in this proof by induction?

I got the first couple of steps correct, but my proof has about 5 extra steps, I didn't know it could be done in 2 steps.

>>8888881
rejected by kek. besides your identity and sexuality should be things you are least concerned with. what you need to be concerned with is your spot in Heaven.

>>8889469
lang algebra. if you were serious about learning you would have known this

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>>8889721
>lang algebra
this?

>>8889711
First step is separating the k+1 term from the whole sum
Second step is applying the inductive hypothesis to the summation
Third step is seeing that F_k+2 + F_k+1 = F_k+3 by the definition of the Fibonacci sequence (add together the 2 previous fibb numbers to get the next)
Last is just realizing that F_k+3 - 1 = F_(k+1)+2 - 1 which finishes the proof

>>8889469
Linear Algebra chapters of Aluffi

You know how Superman can fly around the Earth so fast it reverses the direction it spins in? Would that be possible in real life?

Hey I am an EE student about to be junior in the fall and need to know if it is too late to get into top grad schools by now. Just realized I wanted to do it recently, but have no real research yet. Could I possibly get into top schools like UMich, UIUC, Cornell, etc. with only about 1 year of research?

>>8889950
Forgot to add: I plan to do research summer 2018 for sure and hopefully through the school year 2018-19. Might even spread my last credit hours to stay another semester in fall 2019 to get more research during summer 2019. So at best I'm looking at 2ish years of research. gpa is 3.97 so I am fine there.

>>8889890
thank you

i always feel like i'm stumbling around in the dark with proofs, even at this basic level. i will get better by just trying more proofs though, right?

>>8889959
Yeah, for the most part, you just need more experience with the tricks used in proofs and proof writing in general. Most of the time difficult problems just require more critical thinking, analysis of the problem, or an overall change in thinking. Sometimes taking a break and going for a short walk can help to redirect thinking.

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How can i calculate area of rectangle using coordinates?
I have position of bottom left and top right
btw, cant do something like 4-2 to calculate

>>8890147
(4-2)*(4-2)=2*2=4

>>8890153
read last line i typed
>btw, cant do something like 4-2 to calculate

>>8890156
but you can, i just did it

What is btfo and why isn't it in the wiki search results? Seems important to know

>>8890185
Lurk more

>>8890147
Suppose you have two coordinates which are the top left and bottom right of a rectangle (x,y) and (a,b) respectively
Then the area of the rectangle is (a-x)*(y-b)

>>8890156
Can you integrate y=4 over [2,4] then subtract y=2 over [2,4]?

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This is a super scrub question, but I can't solve this one. I can't just square both sides since that would be assuming what I'm trying to prove.

If I managed to manipulate the equation to somehow be 0 = 0 that wouldn't show it to be true either, since P -> Q having Q be true doesn't show that P is true.

Can anyone help?

>>8890203
do you have a set of axioms you have to work with?

sqrt(a/b) is by definition the non-negative number which squares to a/b, so if you show sqrt(a)/sqrt(b) satisfies that you're done

>>8890203
Isn't this just true by just by the properties of exponents? E.g. (ab)^k = (a^k)(b^k)

If this isn't what is expected, maybe try contradiction

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>>8890208
>>8890210
Sorry, I was being retarded and not looking at the definitions given. I *can* simply square both sides, but not in the way I was originally thinking (multiplying both sides by each other), but by this definition.

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>>8890216
Here's a related question I have about proofs like this in general. To solve this one I can easily just multiply 1 / (1 - sqrt(2)) by (1 + sqrt(2)) to find that it gives the right side. That's nice.

HOWEVER, what I'm wondering is a method where I multiply both sides by (1 - sqrt(2)) and then finding that 1 = 1, which is true, also prove it? I.e. can I prove stuff like this in the same way I solve equations, or am I assuming the truth of what I'm trying to prove here? Or is arriving at a truth (Like 1 = 1) from a supposed truth (Like that in the picture) a proof of the supposed thing?

I know it's a bit of a convoluted question, but it's been bugging me for a while.

>>8890218
>HOWEVER, what I'm wondering is a method where I multiply both sides by (1 - sqrt(2)) and then finding that 1 = 1, which is true, also prove it? I.e. can I prove stuff like this in the same way I solve equations, or am I assuming the truth of what I'm trying to prove here?
no you never start with what you're trying to prove, mainly because once you've assumed that there's no more work to be done, but also just because you arrive at a true statement doesn't mean what you started with was true since some operations aren't reversible

i.e. pretend the question said 'prove that 1/(1-sqrt(2))=-(1+sqrt(3))' instead, you could multiply both sides by 0 to get 0=0 but the initial statement isn't true

>>8890218
>>8890221
also logically
>multiply both sides by (1 - sqrt(2)) and then finding that 1 = 1, which is true
only lets you conclude that IF 1 / (1 - sqrt(2)) = -(1+sqrt(2)) THEN 1=1, it doesn't say anything about whether 1 / (1 - sqrt(2)) equals -(1+sqrt(2)) or not

>>8890221
>>8890225
Thanks my dudes, that's like having a stone lifted from my chest. It's been bugging me for so long, and it never felt right.

I think I got confused because I was seeing questions in the form of If P prove Q changing both sides, which is allowed (right?) and confusing them with questions like these.

The "multiply both sides by 0" example was really good too!

>>8890229
>I think I got confused because I was seeing questions in the form of If P prove Q changing both sides, which is allowed (right?)
yep

>>8889932
i'm not sure but maybe because he doesn't seem to obey newton's third law of motion with the way he flies and if he could maintain a very high speed like close to light speed that would take a tremendous amount of energy and he would push a lot of air

>>8889932
nah

earth has rotational energy of [math] 2.9197 \cdot 10^{33} \space J[/math]

the tsar bomba (strongest nuke) has an energetic release of roughly [math] 2.1 \cdot 10^{17} \space J [/math]

as you can see it would take something [math] 1.39 \cdot 10^{16} [/math] times stronger which isn't exactly realistic

>>8890283
forgot to mention that's only to stop the rotation of the earth assuming 100% transmission of energy into stopping it

>>8890185
Please? I mean I do understand the meaning but everywhere I look for the expansion I get a different answer - bitch the fuck out, bounce the fuck out, etc. Please help a toddler achieve greatness

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Can someone please explain why these answers are the correct answers?

>>8890203

[eqn]\forall x \forall y\left(\left( \sqrt\frac{x}{y} = \frac{\sqrt x}{\sqrt y}\right) \rightarrow \exists z \left(\left(z = \sqrt\frac{x}{y}\right) \rightarrow \left( z = \frac{\sqrt x}{\sqrt y} \right)\right)\right)[/eqn]

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>>8888663
Really stuck on this one.

I started by writing A(Bej) but then i am at a loss.

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Starting pre calc. I understand what absolute value is but i dont get this. absolute value is always positve, right?

>>8890763
>absolute value is always positve, right?
absolute value is always non-negative (i.e. |x|>=0)

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HOW THE FUCK DO I DO THIS FFS?!

>>8890900
calculus brainlet

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Hey /sci/ I'm working on Fourier transformation problems, and in the solutions to one of the problems the following simplification is done.

Can anyone explain how the complex component j ends up in the denominator?

I can see the exponentials have changed place: Before it was exp(-j) - exp(j) and after it is exp(j)-exp(-j), but how does this add the complex j term in the denominator?

>>8890911
enjoy your ban useless faggot :')

>>8890900
Bruh, calm the fuck down, it is not that hard.

Here is what you have to do: take the first derivative of that function and then set it equal to 0.

Do some trigonometry to solve the equation you previously got to 0.

After that, again use some trigonometry to find exactly how many of those solutions lie in the interval (-1,3)

If at any step of this you get stuck you can google or if you want you can report back with your progress and I'll help you a bit more.

>>8890923
at least i know babby's calculus brainlet :')

>>8890919
-j=1/j

>>8890928
Thanks man, I was stuck for hours.

>>8890924
I get sin2x = 1/2 which has only TWO SOLUTIONS FFS. The answer is 5.

I'm assuming it's because the spots will just spill out into the solvent and because ink is a liquid that will travel up the plate whereas pencil lead won't.

>>8890950
That derivative is very, very wrong.
Research the chain rule and the sum rule.

>>8890950
might want to learn how to take a derivative brainlet

do you not even know how to check when you're wrong with wolfram alpha yet? you shouldn't be looking for extrema if you don't know how to derive

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>>8890954

>>8890956
>>8890957
It's not just derivative, I also did trig transformations ffs. Though I've figured out where I went wrong already. I divided by cosine.

>>8890950
>sin2x = 1/2
>only two solutions

babby here
what is the point of universal algebra if we have category theory

>>8890964
Hint that will serve you in the future:
When you are looking for solutions you should never ever ever divide by anything that could potentially be 0 (like cosx). Because when you divide by those things, you remove information for when the thing you divided could be 0.

For example: Imagine if you are looking for the roots of the simple equation x=0
And then you divide by x, that leaves you with 1=0, which "tells" you there is no solution. But that is wrong.

>>8890982
>>8890982
>what is the point of universal algebra if we have category theory
because universal algebra is the study of algebraic structures while category theory is the study of categories, they're two different things

I'm using open office and I've made a table.

I'm counting stuff and write a 1 for every item I see so in the table it looks like

11111111 (etc)

BUT open office converts it to some thing so for example 26 "1"s become 1,11E+025

Now what does that mean? And how do I get it back?

>>8890974
On (-1 to 3) ffs read the fucking posts.

>>8890987
I'm bumping cus I'm desperate guys I need to resolve this asap. I've got several pages of info now that I can't use since I didn't notice the change until now.

>>8890987
>counting in base 1
why though?

Have you tried formatting the cell as text?

>>8891032
It was close on the keyboard, I know I should have probably used like x or something but what's done is done *cries* how do you format it as text?

I just need to know why 26=1,11E+025. If I can figure that out I could probably figure out the rest of my stuff too.

>>8891039
right-click cell > format-cells > far left tab on the format-cells window named "Number" or "Numbers" or something > should be easy enough to find after that

>>8891049
Also you may have to convert to and from numbers and text.

>>8890983
Clearly.

Here's what I get

1 - 2sin^2(x) - 4sinxcosx + 8sin^3(x)cosx = 0

WTF CAN I DO HERE FFS?!

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>>8890919
>>8890928

I understand that by multiplying the expression with -1, I can utilize [math] -j = \frac{1}{j} [/math] to get j in the denominator.

But won't the negative exponential always leave me one positive j component?

See:

[math] (-1) \cdot (\frac{j}{2} \cdot (e^{-j \cdot \omega_{0} \cdot t} - e^{j \cdot \omega_{0} \cdot t} )) [/math]

I will get:

[math] - \frac{j}{2} \cdot (e^{-j \cdot \omega_{0} \cdot t} - e^{j \cdot \omega_{0} \cdot t} ) = - \frac{j}{2} \cdot e^{-j \cdot \omega_{0} \cdot t} + \frac{j}{2} \cdot e^{j \cdot \omega_{0} \cdot t} [/math]

Or am I supposed to say:

[math] (-1) \cdot (\frac{j}{2} \cdot (e^{-j \cdot \omega_{0} \cdot t} - e^{j \cdot \omega_{0} \cdot t} )) = - \frac{1}{2j} \cdot (e^{-j \cdot \omega_{0} \cdot t} - e^{j \cdot \omega_{0} \cdot t} ) [/math]

But then how can I choose this and not the other? Do I decide based on what makes most sense in the expression?

>>8891077
That is either not the derivative, or it is not completely simplified.

Use wolfram alpha to get the right form of the derivative man.

>>8891077
lmao how can you be this bad at taking a derivative brainlet? please show your steps so i can laugh at how badly you got it this wrong

>>8891079
the second one ((−1)⋅(j/2⋅(e^(−j⋅ω0⋅t)−e^(j⋅ω0⋅t)))=−1/2j⋅(e^(−j⋅ω0⋅t)−e^(j⋅ω0⋅t))) is wrong, you didn't get rid of the negative when you moved the j into the denominator

>>8890640
>Really stuck on this one.
>I started by writing A(Bej) but then i am at a loss.
By definition of product:
[math]C=AB[/math]
[math]C_ij=\sum_k A_{ik} B_{kj}[math]
[math]A_{ik}=a_k[/math] by your definition of the last. Finally
[math]Ce_r=C_{ir}=\sum_k A_{ik}B_{kr}=\sum_k a_{k}B_{kr}[/math]

>>8891083
No fucking shit it's not completely simplified. The question WHAT ELSE CAN YOU DO HERE FFS?

>>8891084
You fucking retard the derivative is
> 2cos2x - 2sin4x

That much is fucking clear.

Question is WHAT CAN YOU FUCKING DO?! It has to be either parenthesised out or only same function of the same angle. BUT IT DOESN'T GET THAT WAY.

>>8891093
>WHAT CAN YOU FUCKING DO?!
set it to zero and solve for x brainlet, is this your first finding extrema problem?

>>8891084
>the second one is wrong, you didn't get rid of the negative when you moved the j into the denominator

True, thanks.

The thing is though, that if I get rid of the negative by putting j in the denominator, then I can't change the signs of the exponentials.

So then how the heck do I end up with this expression:

>>8890919

>>8891103
you seem a bit confused but here:

(j/2)(e^{-jwt}-e^{jwt})
= (-j/2)(e^{jwt}-e^{-jwt})
=1/(2j) (e^{jwt}-e^{-jwt})

>>8891098

You idiotic fucking shithead HERE'S WHAT I FUCKING GET >>8891077

WHAT CAN YOU DO ____HERE____ FFS?! Clearly fucking nothing since all you do is just shit talk like a 5 yo faggot.

>>8891109
Ah okay, so you just switch the sign of all the components in the expression.

This makes more sense than to multiply it by (-1).

Thanks a million!

>>8891113
but setting that expression to 0 and solving for x doesn't throw in all those other terms brainlet, why do you overcomplicate things with useless trig identities?

don't you know what sine and cosine look like brainlet? just draw a picture and you'll see the five points

>>8891113

I THINK I GOT IT FFS

> 4sin(x)cos(x)cos2x = cos2x

www.wolframalpha com/input/?i=4sinxcosxcos2x+%3D+cos2x;

BUT WHAT THE FUCK DO I DO NOW?! HOW SOLVE THIS SHIT?

>>8891136

FFS you're right, thanks.

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So anyway what's up with this fucking shit?

There's two negative answers: -1 and -1.5. YOU CAN FUCKING GUESS WHICH ONE IS THE BIGGEST.

And yet they say it's -1.5

Is it just them being fucking retarded illogical cunts? Or am I missing something this time?

When doing trig substitution what happens to dx and boundaries?

For example.

INTEGRAL^2_1(sqrt[2(1 - (x/2)^2])dx = { x/2 === sint} = INTEGRAL^?_?(sqrt[2]cost)d?

Re-asking as no one answered me last thread.
I want to get far in optimization (in real domain).
Currently I have studied real analysis, convex optimization.
I'm thinking about getting to work on some differential geometry books.
Will they help?

>>8891185
doesn't matter what kind of substitution it is, for any substitution you get the boundaries the same way, plugging it into the substitution

i.e. if x=1 then sint=1/2

>>8891195
So it would be INTEGRAL^(pi/2)_(pi/6)(sqrt(2)cost)dt?

>>8890352
Blown the fuck out
now fuck off

>>8890957
>derive
I hope you know that differentiation is different

>>8891224
of course, but people still understand what you mean with derive

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How do I get the volume of this cunt? I got the area, so do I just integrate it and that's it?

>>8891268
Can you translate to english to give more context?

>>8891268
Volume of revolution? if so search for disk method and shell method. This kind of stuff has very nice visualizations

>>8891268
cause that's clearly not fucking it

What is recommended book on algebraic number theory?

>Pennsylvania University, Philadelphia
>Mellon University, Pittsburgh
Out of these two options for ENGINEERING, which one do you think would give me a higher chance of working in Japan? Provide reasoning and proofs for bonus points.

>>8891289
Do some research on whether they have exchange program with a Japanese uni.

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>>8891286
what's your background?

murty/esmonde's 'problems in algebraic number theory' is a good 'build the theory by hand' book

cohen's books are good for the constructive/computational point of view

for general texts can recommend neukirch's 'algebraic number theory' and ribenboim's 'Classical Theory of Algebraic Numbers'

>>8891270

It doesn't matter basically they want the probably some point will have bigger X than 1 on a ball that's acquired by spinning this shit around X-axis and filling it multiplied by 32.

>>8891306
So I integrate the graph from 1 to 2, then -2 to 2 and get

>>8891310


But what now?

WHAT THE FUCK IS WRONG WITH SQRT WHY THE FUCK IS IT FUCKING FILTERED

>>8891300
Relevant courses at the undergrad level I've taken are one year abstract algebra, term of rep theory, term of complex analysis, term of topology, and term of introduction number theory (type that has no analysis/algebra requirements).

Slightly intimidated by graduate level texts, but I've got nothing to lose.

>>8891310
SQRT2DIVIDED BY2 and 2SQRT2.
>>8891315

CAN I NOT WRITE FUCKING /

WHAT THE FUCK IS WRONG sqrt(2) 2 and 2sqrt(2).

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>>8891322
ribenboim + murty might be a good pair to start with then

>>8891335
WHO THE FUCK WOULD BAN /2 ?!

>>8891339
>>8891335
>>8891330
>>8891323
>>8891330
>>8891320
are you autistic?

>>8891300
>>8891336
Thanks. Excited to start

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>>8891347
try writing picrel

>>8890147
bottom left:(x1,y1)
top right:(x2, y2)
equation:(x2-x1)*(y2-y1)

>>8891377
sqrt(2)/2
2sqrt(2)

and

>>8891274
Yeah.

So I tried disk method and I get NEGATIVE VOLUME FFS.

Look.

INTEGRAL^2_1(pi(-x^2 + 2))dx = -pi/3. WTF?

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Is it considered incorrect to represent R -> R2 relations like this? Professor didn't take points off, but said it was abnormal.

>>8888663
https://www.youtube.com/watch?v=dYaNQ1R77Ug

>>8891490
No, your solution is fine. And I think "abnormal" is the wrong word.

>>8891490
I would have taken points off
If you were in multivariable calc I wouldn't though

>>8890958
refraction?

Does the fact that integrals are a type of infinite series mean that you can find the closed form to some infinite series by writing it in terms of an integral, then finding an antiderivative?

>>8891596
No.

What is the meaning of life?

>>8891596
yep

>>8891574
Explain why you find it acceptable in multivar and not in singlevar

>>8891620
Personal choice.
Need a recommendation?

>>8891650
I choose to roll a train on your mom ahahah

How do I solve an infinite state mealy machine?

>>8891765
your mom already rolled over me.

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What is a good R course?
>inb4 Coursera
it fucking sucks

>>8891490
and t goes from where to where? That's important since it gives the direction

So you can take e, which can't be calculated exactly by itself, then raise it to the power of pi*i, which also can't be calculated exactly by itself, and get a number that you can write the exact value of(-1).

My question is, are there physical systems that behave more "cleanly" as a whole(can be described in terms of algebraic numbers) despite having individual pieces that can only be described in terms of transcendental numbers?

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So, just the wallpaper group, no?

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>>8891845
>which can't be calculated exactly by itself,

>>8891047
E+025 means "times 10 to the 25th power", since it's a large number, it rounds the ones up (down).

>>8891845
It makes perfect sense, study some complex analysis.

>>8891812
Is this b8? t isn't spatial. It's independent of x and y.
You could represent it graphically as a path. Pick any value of t and place a point whose x is whatever is in the term with xhat, and whose y is whatever's in the term with yhat.
As you plot many values of t, sufficiently close to each other, you'll find that they trace a circle, in this case.
Look up parametric equations and vector-valued functions.

https://youtu.be/1ENkP0h8nAg?t=325

If time is moving slower at the bottom of the box, due to the stronger gravitational field, shouldn't it take more time between the photons? I don't understand why it would be otherwise, can someone explain?

>>8891881
>>8891812
I just reread this reply. Sorry.
fvec is valid for all real t. It's implied that the direction of the circle is the path fvec takes as t increases, like how we could say of an algebraic function y of x that it increases over an interval (without specifying that it increases _as x increases_.)

>>8891881
I fucking know t isn't on the plane.
I mean where do you start with t? What is it's last value after going 4 times counterclockwise?
[math]\theta_1 \leq t \leq\theta_2[/math]

Say i have a tube of water, sealed both ends. I want to generate standing waves by vibrating one end. What is the equation that describes this system? What frequencies cause standing waves in a given length of tube? What if i have denser or thinner liquids in the container? Does the diameter have effect on the system?

>>8891893
the direction is important for line integrals, if you ever study that.

>>8891893
There is no "first" or "last" value. It's defined for all real t. You could begin and end with any t you'd like as long as they're real numbers.
It's just that because sine and cosine are cyclic, infinitely many t can trace to the same x and y.

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how do i find k in pic related? using the first point i got 16 as by the pigeonhole principle two must be the same. i dont see how to use the second point as surely the integers could all be 1s in which case it would never be true. am i reading it right?

>>8891917
>am i reading it right?
no

> the integers could all be 1s in which case it would never be true.
but it would be true because it satisfies the first point

>>8891490
>a set of parametric equations
in this case i think it's very strange, bordering on incorrect

>>8891915
Yes, there is a first and last value. You need it to go exactly four times, in exactly the counterclockwise direction. How would you specify this otherwise?

>>8891893
>>8891948
t1 + 2pi = t2

f(t1) = f(t2)

How do I assasinate Trump?

What is the "first mystery" of mathematics; if somebody were to start building mathematics from scratch, what is the first thing they would run into that makes them question the nature of math?

My first thought is the pattern of the prime numbers, but that's just because it's a mystery that still hasn't been solved today.

>>8891965
If I was a caveman the first thing that wouldn't feel intuitive to me would be complex numbers.

>>8891965
>What is the "first mystery" of mathematics; if somebody were to start building mathematics from scratch, what is the first thing they would run into that makes them question the nature of math?
whether 0.999...=1

If I'm looking to work on industry should I graduate in civil or mehanic engineering?

>>8891965
what does the nature of math even mean?

what's the real meaning behind the unsolved mysteries of math, like pattern of prime numbers, riemann hypothesis etc?

is our conception flawed, or are we have not yet discovered some universal principle or what?

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Is it possible to make synthetic hydroxycitric acid from citric acid? If so, what should I add to it and how should it be prepared?

I had Organic I and I feel retarded asking this because I should already know this but it's bothering the shit out of me.

>>8891965
Constructing angles probably

>>8891965
Zeno's paradoxes

>>8891917
kmin= 2
i= 1
j= 2
x1= xi= 1
x2= xj= 15
i /= j
xi + xj= 16

>>8892046
so wrong it hurts

it's for any set of k integers, not a specific one

it's not k=2 since {1,3} don't satisfy the conditions

>>8892067
Well, fuck
Sorry anon
If the second condition can never be guaranteed then >>8891940 must have gotten it right, it's an xor relation between them

>>8891917
Consider all pairs x,y such that x+y=16 and argue that if you have more than k unique values (otherwise you are in case 1), you are guaranteed that you have at least one such pair.

>>8892106
x1... xk are not necessarily unique

>>8892176
If they are not you already satisfy the first bullet.

If I'm looking to work on industry should I graduate in civil or mehanic engineering?

Does tan() have alternate uses like sin() does, or is it just used for its original purpose?

>>8892216
Examples of what you mean by "alternate" use?

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If anyone here knows algebra, help would be much appreciated.

So, a) is fine, b) I'm not so sure about. "F = Z_7(alpha)" is not meant in the literal sense of equality, but as an isomorphism, right? As in, those two fields are isomorphic. Anyway, the basis, using alpha, would just be {1, alpha, alpha^2} = {1, x + <f>, x^2 + <f>}, or? The number of elements being 7^3.

If I'm looking to work on industry should I graduate in civil or mehanic engineering?

>>8892257
>"F = Z_7(alpha)" is not meant in the literal sense of equality, but as an isomorphism, right?
i think it's equality

>Anyway, the basis, using alpha, would just be {1, alpha, alpha^2} = {1, x + <f>, x^2 + <f>}, or?
looks good (obviously there's many possible bases)

>>8892280
>i think it's equality

Actually yeah, now that I think of it. For some reason I was thinking of alfa as an element of Z_7.

>looks good (obviously there's many possible bases)

Okay, nice. So, say I wanted to express alpha^5 in terms of the basis I found, would that just be x^5 + <f>?

>>8892293
> So, say I wanted to express alpha^5 in terms of the basis I found, would that just be x^5 + <f>?
no because you didn't write it in terms of basis elements

>>8892303
hurrr, I'm thinking with poo clogging my brain. So, I did some trickerooing and found that (let's just say alpha = a) a^5 = 5a^3-a^3.

Hence a^5 = x + <f> (5*(x^2+<f>) - x + <f>), yaya?

>>8892333
5a^3-a^2**

>>8892333
it should be written x*1+y*alpha+z*alpha^2 for some x,y,z in Z_7

Mach's principle and inertial frames of reference.
Explain

>>8891643
Writing vector functions as multiples of basis vectors is normal in multivariable whereas in single variable the question clearly asks for equations (plural)

>>8892365
https://en.wikipedia.org/wiki/Mach's_principle
https://en.wikipedia.org/wiki/Inertial_frame_of_reference

>>8892374
Wow you're such an expert

>>8892376
It's not clear at all what you're having issues with, all you said was 'explain'

>>8892388
Sorry
I'm a little drunk and I've made a few threads on this topic and have never gotten a response

My issue is that how does matter know what that frame of reference is?
Are there superluminal mediating particles?
Clearly impossible.

Why is knowing the domain of a function important?

>>8892405
so that you know what inputs you can put into the function to actually get outputs

So why exactly is Fluid mechanics/dynamics still an issue?
I remember there being an unsolved bit to it, can anyone refresh my memory or at least provide me with tips on what to google?

>>8892461
Navier–Stokes?

If I'm looking to work on industry should I graduate in civil or mehanic engineering?

>>8892461
Why is a triple pendulum unsolved?

>>8892461
work through the proof again and look for the part where they say [math] Q_{x+\Delta{x}} \approx Q_{x+d{x}} [/math]

thats why.

when estimating functions like with fourier series, why is it necessary to use harmonics? what really is harmonics? why are harmonic functions only related by integers and not fractions? I mean like with cosine and sine fourier series, you only sum integer frequency multiples.
also, is fourier series only cosine or sine? can you transform any function to fourier series?

>>8892545
Fourier series are similar to Taylor functions except instead of using x^n as your basis you use e^(i*n*x*2pi). These complex exponentials are a nice orthnormal basis on the L^2 functions on the interval [0,1].

Naturally there is a different procedure of figuring out coefficients, convergence, etc. But it leads to a decomposition of functions

in the standard form of an equation: Ax + By = C,
what does C represent? I desire to understand it intuitively, and the C does not make sense to me.

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how much does a shitty community college transcript really matter? I don't expect to get into ivy league or anything of course, but will it be covered up after I get nothing but straight A's my final two years at uni?

>>8892624
I believe most institutions only count institutional credit towards gpa calculations.

>>8892624
>>8892624
I'd like to be able to go for a PhD though, and ideally the nicer the school the better. I'm putting a lot of time into building my resume outside of my grades, in addition to being certain I pull only A's in my remaining time at community college and continue to so during uni. I did the math and I get a cumulative of around 3.8 still

>>8892577
it depends on whatever you're defining A, x, B, y and C to be, of course, but usually a constant. That being said it could be any variables, like ":)", ":3", "!", etc..


>>8892628
Oh that's good to hear, I've heard this and I've heard that they count altogether too though.. When you say institutional credit, you mean at that institution, right? As in, PoDunk University will only calculate GPA for credits I earned while there?

What about potential grad schools?

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Why would the build-up of potassium inside the cell (due to KATP channel inhibition via ATP) lead to depolarization? Wouldn't the cell be hyperpolarized instead?

The only plausible answer I think is that the cell depolarizes due to potassium's positive charge, but then I don't understand how this is different from creating the resting potential, causing it to be -70 mV.

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If these brackets denote intervals on the Real line, does this series describe all positive real numbers, or is there something nuanced about "interval" that would exclude some numbers?

>>8892577
If we consider ax+by=0, then we have graph passing through origin. We note that ax + by = (a, b).(x, y) = 0 which implies points on the line are perpendicular to (a,b). We can now consider translating this line. This preserves this perpendicularity property. The value C, then, decides which of the infinitely many lines that arise from the translation of ax+by=0 we want.

To see that one value can decide the line, consider translating the line in the direction of the normal vector. In fact, if you normalize (a,b) to get (a', b'), you notice that translating the origin to c(a', b') gives you

a'(x-ca') + b'(y-cb') = 0
a'x + b'x = c(a'^2+b'^2) = c|(a', b')|^2 = c

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I read through first 8 chapters of Eulers Elements Of Algebra and then got to these practice questions and answers and I dont know how find these answers or why they are correct. Did I miss something and should I go back and start over at chapter 1? How fucked am I that I didnt already come to be able to understand this?

>>8892696
that's not a series, it's a union
it's [0,2] union [1,3] union ... [2,4] union... which equals [0,infinity)

>>8892713
can you not even do the first one? it's pretty straightforward simplification

>>8892726
No not the first one. The closest one I've come is no 4 I but I get -1 instead of 1 as the numerator. So it's pretty bad?

>>8892733
if you cant do 1 there's an issue

it's literally just
(cx+x^2)/(ca^2+a^2x)
=x(c+x)/[a^2(c+x)]
=x/a^2

>>8892733
You probably overdid 4 by expanding everything.

You should know x^2-y^2 = (x+y)(x-y). Use that for both the numerator and denominator. Then it simplifies easily. You should do these and similar problems until they are kind of second nature.

>>8892733
also idk how you get a -1 anywhere
(x^2-y^2)/(x^4-y^4)
=(x^2-y^2)/[(x^2-y^2)(x^2+y^2)]
=1/(x^2+y^2)

>>8892723
sorry, so i thought i was interpreting this union correctly, in the sense that it's kind of like a series, however, as you corrected me, it's actually a union of intervals.

that union goes on towards infinity, but it is a discrete sampling of the real line? how would you describe this in more formal language if a set S were to be equal to the Union >>8892696

>>8892736
Oh I kinda see what you're doing there, but I dont think it was really covered in this book yet. Recall this book was published in the 1700s so any number of things could have gone wrong like I misunderstood the early modern English and notation.

>>8892744
Yeah actually I was trying to expand stuff.

I dont think I should go on to the next chapter because this is the kind of stuff why self study has such a stigma because people skip on when they dont really have a grasp yet.

>>8892767
Very well said. Grind out these problems to build your intuition and toolbox

>>8892745
I kinda see what you guys are doing here, this is like what modern textbooks call FOIL, but I dont recall Euler discussing it in this book or maybe I missed it completely or misunderstood it.

>>8892777
FOIL is just a mnemonic to help remember how to multiply two binomials. It's actually just the distributive property.

You should know how to multiply (x+y)(x-y). Working backwards (factoring) is the hard part which requires a bit of practice.

>>8892784
Yeah when I saw these replies posted it started to come back to me I vaguely recall about (x+y)(x-y) but HS algebra was many years ago.
I was just working through Euler because he is one of the greats, and Element of Algebra is supposed to be pretty elementary.

I don't drink coffe but drink sometimes substances with caffeine (aka energy drinks), if I did it more often would my body get used to it? I suppose yes but how much is the limit of caffeine per day to still get that "wake up" effect from just 1 average coffe?

It is useful to keep track of the caffeine half life?


Tldr: How do I make sure my body does not get used to caffeine beyond just saying "don't drink it everyday"?

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>>8892784 >>8892773 >>8892745 >>8892744 >>8892736
I guess Im going to have to have to go back to a previous chapter because I guess I missed something but Im not sure how many chapters I should redo. Do any of you know which chapter Euler covers this?

What would be the best way to ask a professor for an undergraduate research opportunity? Email? In person? And should I at least have a class with them or just ask anybody I can?

What exactly do Gödel's incompleteness theorems imply?

>>8892881
Any framework which can describe the natural numbers and do arithmetic on them will have statements which are true within the framework, but are unprovable

>>8892914
Is it implying that if you try to prove them you will contradict the system, so you basically take certain parts of the system "on faith?"

>>8892917
No. If you were to arrive at a contradiction you would know it were false. The idea is that something is actually true, in the same sense that something which is proven is true, just that there is no way to prove that it is true.

>>8892945
Okay, so I'm having trouble understanding why that is. If you would be so kind, could you give an example?

>>8891917
There are exactly 8 pairs of integers between 1 and 15 that sum up to 16 (1 + 15, 2+14, ... 7 + 9, 8 + 8).
Since every integer between 1 and 15 occurs in exactly one pair, k may at most be 8 such that this property does not hold, and it must hold for k = 9

>>8892956
It follows from Godel's proof. It is supposed to be totally counterintuitive. I believe his proof is non-constructive anyway so there is no example to give. You also couldn't verify an example anyway.

>>8891113
Yo shut the fuck up please

>>8892222
>Nobody chex these QUADS
Truly reddit has taken over

>>8893013
we check primes here btw nice prime

>>8893027
U 2 mange

>>8893033
$ factor 8893013
8893013: 8893013
$ factor 8893027
8893027: 11 13 62189
$ factor 8893033
8893033: 8893033

>>8893013
>>>/bant/

If I'm looking to work on industry should I graduate in civil or mehanic engineering?

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Can someone please explain why we can use a factorial here to determine the determinant and where the value 5 comes from?

This looks like easier method than finding all the inversions, but would like to know exactly how 5 is determined

>>8893116
determinant of a diagonal matrix is the product of its diagonal entries (you should show this)

Remains unsolved on stackexchange, anyone help me out?

https://math.stackexchange.com/questions/2270107/how-to-show-the-euclidean-algorithm-for-gaussian-integers-generates-a-gcd

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>>8893154
forgot image

>>8893126
Yes, I understand this, but how do you determine exactly when the determinant is positive or negative?

I imagine you multiply by (-1)^n the factorial, but can n just be the number of times you flip the rows around or number of inversions?

Because there are 7 inversions here, while rows are flipped 3 times. Can I just the number of times I flipped the rows around for my value for n?

>>8893116
In the definition of the determinant it is included that if you multiply one row (or column) of the matrix A by any number b the determinant of that matrix that you get is b*determinant(A).

Multiply the first row of the identity matrix by 5 the second by 4 and so on then you will get the matrix.

In the end you have 5*4*3*2*1*det(Identity)=5!

>>8893166
>can n just be the number of times you flip the rows around or number of inversions?
Yes, it is.

>>8893201
So it can be both?

can you take a shit on the moon? what about the inertia? is it possible?

>>8893227
>So it can be both?
The idea is the following:
I have a non-diagonal matrix.
It can be rearranged to give a diagonal one.
Each time a row is exchanged, the determinant remains the same up to a sign flip (the same is true for columns).
The determinant of a diagonal matrix is just the product of the diagonal elements (in your case 5*4*3*1*2=5!).
You have performed 5 swaps, therefore there is an extra (-1)^5 factor, giving at the end -(5!).

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recommend some reading material on fourier transforms pls

what the frick is this?
>https://reference.wolfram.com/language/ref/FourierParameters.html

how can i plot the frequency response of sinc(x) in mathematica?

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how to plot this in mathematica?

If I'm looking to work on industry should I graduate in civil or mehanic engineering?

>>8893156
Tell me about that font rendering.

Look at how eucledian algorithm works on integers. Recall Z[i] is an eucledian domain (implies PID which implies UFD). Can you use these properties to generalize the ideas of Z to Z[i]?

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Haven't taken a math course in 3 years and have "forgot" quite a bit. I essentially need a refresher from algebra thru calculus ii

Anyone have a recommendation as to where I could find one?

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What is the best way to get into the oil/mining industry as someone who is a physics major that goes to a top 10 worldwide university?

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How to find volume of the body of revolution? Disk method gives negative when trying to calculate part of the ball with X > 1. So clearly that's not the way to go.

If I'm looking to work on industry should I graduate in civil or mehanic engineering?

>>8893403
>How to find volume of the body of revolution? Disk method gives negative when trying to calculate part of the ball with X > 1. So clearly that's not the way to go.
Explain the problem better. And translate it accurately.

>>8893403
Why don't you translate the curve entirely into the first quadrant?

>>8893418
This. Yesterday I thought you were looking for the sphere.

>>8891817
>>>8891113
>>>8891144
>>>8891171
>>>8891268
>Jesus Christ not this fucking faggot again.
Guess who is here again.... And with the same question than yesterday.... (Yes, I'm also tired of him and his retardness)

>>8893436
>>>8893418 (You)
> This. Yesterday I thought you were looking for the sphere.
The first think I though when I saw this problem was: Body of revolution.... With respect to what axis? If I choose the X-axis as my revolution axis I get a sphere but if I choose the Y-axis I get a hemisphere....

>>8893403
you want the volume of a spherical cap with a height of 1 on a sphere with a radius of 2?

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how does this make sense?

>>8893489
its a typo (if you mean (c))

Trying to teach myself math and getting stuck on the basics. Never thought Id miss having professors to talk to.
Can someone explain continuous functions between spaces
[math]f:Y\rightarrow X [/math]
[math]X\subset R^1 [/math] and [math] Y \subset R^2[/math]
Say
[math]x\in X[/math]
[math]f:(x)\rightarrow (cos(x),sin(x)) [/math]
Is this path connected. Furthermore is it also a homeomorphism.

>>8893513
Meant to ask if it was continuous, but those as well.

>>8893513
i guess you meant f: X to Y but whether it's path connected depends on X

i.e. if X = R^1 then f(X) is a circle
if X= [0,pi/2] union [pi, 3pi/2] then it's two disconnected arcs of the circle, so not path-connected

pretty sure it's a homeomorphism

and yes it's continuous because each component sin(x) and cos(x) are continuous

>>8893524
>>8893513
actually maybe not necessarily a homeomorphism (i.e. if X= [0, pi/2] union the point {2pi+pi/4})

>>8893513
I assume you mean f: X -> Y and not what you wrote.

The map f is continuous.

It is not a homeomorphism. If X=[0,2π) and Y=S^1 then it is a continuous bijection, but it does not have a continuous inverse.

>>8893524
Thanks, the book I have uses a "non intuitive" definition of continuous so I was over complicating it.
>>8893542
Can you elaborate a little more on not having continuous inverse.
Is it because f'(Y) is a proper subset of X.

So say x is cos(phi). Is it now a homeomorphism since f':(a,b)->(a) works?

Sorry if Im being dumb, just want to make sure I understand before I keep going.

Three body hohmann transfer problem using patched conics approach. Transfer from LEO to Orbit around the Sun To Mars. Include delta V required for maneuvers.

>>8893586
Wait take it all back, example just doesnt work for f.
Its making more sense now. Ignore
>So say x is cos(phi). Is it now a homeomorphism since f':(a,b)->(a) works?

Neither arccos or arcsin are continuous.
However if we restrict the domain of X to the continuous part of arccos would it be homeomorphic. Say [0,1]

>>8888663
OP you idiot. Only post the math oracle. Not your retarded frog may mays.

>>8893643
quit forcing that crap, it got deleted >>8887234

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???

Let R = { a + bi | a,b ∈ a }, where i has the usual meaning of i^2 = −1 (these are sometimes called Gaussian integers). Determine the number of cosets in R/<5>, where <5> is the ideal generated by 5 = 5 + 0i.

help

>>8893952
>a,b ∈ a
I mean a,b ∈ Integers

Why is pi NOT 22/7?

>>8893602
Seriously, no one here understands astrodynamics?

>>8893952
where are you getting stuck? it's a pretty straightforward calculation

>>8893987
Is there not infinite? <5> is all the gaussian integers that are multiples of 5 right? So isn't there an infinite number of cosets of that ring?

>>8893994
>So isn't there an infinite number of cosets of that ring?
yes

>>8893981
Why would it be?

Pls help. How is the unit group U_7 = {1, 2, 3, 4, 5, 6} cyclic? What's the generator?

>>8894023
stop being lazy brainlet, it literally takes like 2 seconds to calculate the subgroups generated by each element to find a generator

>>8894023
>The group is cyclic when n is a power of an odd prime, or twice a power of an odd prime, or 1, 2, or 4.

Anyone good with groups.
I keep seeing lorentz groups with notation SO+(1, 3).
I know what SO is. I dont understand why it has two parameters.

>>8894045
https://en.wikipedia.org/wiki/Indefinite_orthogonal_group
>O(p, q) is the Lie group of all linear transformations of an n-dimensional real vector space that leave invariant a nondegenerate, symmetric bilinear form of signature (p, q), where n = p + q

https://en.wikipedia.org/wiki/Lorentz_group#Basic_properties

>the Lorentz group may be described as the generalized orthogonal group O(1,3)

>Lorentz transformations that preserve the direction of time are called orthochronous. The subgroup of orthochronous transformations is often denoted O+(1,3).

>The subgroup of all Lorentz transformations preserving both orientation and direction of time is called the proper, orthochronous Lorentz group or restricted Lorentz group, and is denoted by SO+(1, 3)

>>8894045
It is essentially the Isometry group of Minkowski Space modulo translations.

>>8893925
Stuck on the starfish. Is that 4 or 5?

>>8893925
you have to consider imaginary numbers for this to make sense

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>>8893925

>>8894087
Proofs?

>>8894054
Ive read about it. But I just cant grasp what that means. I fully understand On(R) and could do proofs about it on the spot. I get that O(p,q) is related, but I dont get how.
>>8894060
I understand physically what it means. But not mathematically.
Maybe it would help if I saw a path through it, or an element of the group.
Like a path through U(1) can be written as {e^it}. What form would O(p,q) even look like.

are inductively generated sets always the least sets that satisfy that property?

does the same apply to structural induction?

Can someone explain to me why i is defined by i^2 = -1 and not simply i = sqrt(-1)?

>>8894110
>I understand physically what it means. But not mathematically.

>I understand physically what it means. But not mathematically.

Mathematically it is exactly what I said.

[math]O\left( {3,1} \right) = \operatorname{Isom} \left( {{\mathbb{R}^{3,1}}} \right)/T\left( {{\mathbb{R}^{3,1}}} \right)[/math]

Where [math]{{\mathbb{R}^{3,1}}}[/math] just means [math]{\mathbb{R}^4}[/math] taken with the Minkowski metric instead of the Euclidean metric.

>>8894128
[math]i^2 = -1 [/math] is much cleaner. But that is a personal reason, the real reason would be:

In a formal introduction on complex numbers, i would not be defined like that. You would first define the set of complex numbers using some set theory. After that you would identify a certain element and call that element i. After that your professor will ask you to multiply that element with itself, and then you will see that the result is the complex -1. And thus you get that property, which is more a theorem than a definition.

>>8894128
Because they do not mean the same thing.
x^2=4 does not mean x=sqrt(4).

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>>8894095

Is there a site and/or small program that can show viable operation to obtain a specific results given specific data?
i.e if i want to obtain 704, and i have 8, 22, 5 and 20, i can just input those into the site and i'd get something like (22*8*20)/5

Two of these statements are false:

1. If G is an infinite group, then G contains an element of infinite order.
2. If K is a subgroup of H and H is a subgroup of G, then K is a subgroup of G.
3. If S is a subring of R, and R has characteristic k ≠ 0, then S has characteristic k.

I know 3 is false. 2 Has got to be true. But what's a counterexample for 1?

>>8894157
holy schitt

In Uni, will my math classes have 'projects' and 'attendence' that count towards my grade?

Really rustles my jimmies that not showing up lowers my GPA

>>8894170
https://en.wikipedia.org/wiki/Grigorchuk_group

The real challenge will be how you will convince your professor that you actually came up with that.

>>8894184
Seen very few of these. For projects it's usually a group or independent paper (nothing novel) of a related topic. As for attendance, only in the class that teaches technical writing/presentation/collaboration skills.

>>8894170
what about the subgroup of O(n) consisting only of rotations by a rational multiple of pi

Can someone show me how to do a three body hohmann transfer problem? Transfer from Earth to Mars. Using patched conics approach to astrodynamics.

>>8892696
>>8892756

Unions are statements about series, they aren't series themselves.

>>8888663
Is there an equation for the probability that a particle has to quantum tunnel, and if so, what is it?

>>8893368
You really fucked yourself there anon. With a physics major, there is no way you could get in the oil/mining industry. If you are desperate, then redo univ and go for a business major or someshit. Also, maybe >>>/adv/ can help.

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>>8893925
I think its like this.

>>8894172
Anon thats wrong im pretty sure >>8894294
is right

>>8893418

FIND THE PROBABILITY OF AN ARBITRARY POINT IN THE BODY OF REVOLUTION OF THE GRAPH (BALL FFS) HAVING X > 1. THEN MULTIPLY IT BY 32.

>>8893419
Why the fuck would I do that?

>>8893436
No, I always said it was a ball.

>>8893442
Stop being such a try hard bitch. You're not fooling anybody with your pathetic samefagging attempt.

It's a thread specifically for people like me: who get stuck on problems and share their progress while asking for help.

I don't even normally do this, but I got a life-or-death test very soon.

So stop being such a butthurt little whiner who shits this thread because his life sucks. Thanks.

>>8893456
I just want the volume of a ball of radius 2 AND volume of it's part every point of which has X > 1.


Now the formula for the graph is obviously sr[2 - x^2], so using the disk method we get pi[2 - x^2] the 1 to 2 integral of which is NEGATIVE. So I wonder HOW THE FUCK is it the case?

>>8894300

For some reason circle parentheses are filtered - at least with x^2) near them or something. I don't know WHAT the fuck is wrong here exactly.

Retarded fucking autists.

Bought these at a yard sale in a college neighborhood, is there a possibility of them still having remnants on them from previous use which can't be washed off by soap+water and then a rinse?
My layman's ignorance leads me to believe it would have damaged the glass in some way
I can see if it was able to stick around after being cleaned by the student

File: glass.png (956KB, 590x906px) Image search: [Google]

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>>8894310
also I remembered to forget the picture again

>>8894300
m8, you want to use r^2 - x^2. Radius is 2 so you get 4-x^2

>>8893325
khanacademy.fuckjews

>>8894312
Unless they poured fucking liquid uranium/plutonium in there you should be fine, which they probably didn't.

>>8893925
>>8894061
>>8894071
>>8894087
>>8894294
>>8894095
>>8894157
>>8894172
>>8894297
this

>>8894320
out of curiosity then;
Is there anything that can dissolve the type of glass these are made out of?
Chemists seem to always use glass so I assume it's pretty non-reactive

>>8894300
>I don't even normally do this, but I got a life-or-death test very soon.
you will fail

>>8894327
flourine

>>8894327
Hydrofluoric acid will rape glass

>>8894315

Hahaha thanks it was so simple!

File: WTFDTM.png (2KB, 191x36px) Image search: [Google]

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What are the FIRST n whole numbers (negative and positive integers, and zero)? They want me to take a median of the first n whole numbers of picrel, and I've tried 0 to 8 (1 to 9 obviously doesn't work), -4 to 4 - and they don't give me fucking zero which is the answer.

Look:

-5 -4 -3 0 3 5 5 12 21 Median is 3.

WTF?

How do you get line = slope*tg(angle)?

what's the number of partitions of {1,2,3,4} which don't have 2,3 in the same part? without exhaustively listing them all, I don't know where to start. I've not encountered bell numbers btw

Hello, in Partial fraction decomposition, how do we know if we must write aX + b or just a ?
https://wikimedia.org/api/rest_v1/media/math/render/svg/8c18778b44345f82e92176813858c6c8c25fdd11

>>8894457
It depends on the degree of the polynomial in the denomination. If it's linear (1st degree polynomial) you write A, if it's non-linear (degree >1) you write Ax+B

Just started reading algebraic geometry book and it's like 99% algebra and 1% geometry

Why

>>8894623
thanks for your answer but i have a correction where it's marked a/(x-1)^3
So when it's (1st degree polynomial)^n, it's considered to be a 1st degree polynomial i suppose ?

File: kp.png (31KB, 269x471px) Image search: [Google]

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pls help find KP

>>8895150
Are the units on the grid reliable? If so, you can calculate the area in two ways, using LK as the height and using KP as the height.

There may be some similar triangle argument but I forget.

>>8894288
How did I fuck myself? I honestly though my physics major could be useful with geophysics and I can get into petroleum exploration and shit and work myself up?

>>8895167

It's not about the grid. I don't need area I need KP.

>>8895208
A = bh/2

If you have A and b you can solve for h. Figure out the area of the triangle and use KP as your height as in A = 12|KP|/2 and then solve for |KP|

>>8895219
Well how the fuck do I know the area?

>>8895234
That's why I was asking about the grid. You can get the lengths of the two missing sides if you rely on the grid.

>>8895238
Well you can't rely on the fucking grid, that much is clear.

>>8895250
> that much is clear
Why? KL and KM look grid-aligned

>>8895254
Cause you're not supposed to. I'm sure you could also use a fucking ruler and figure it out by proportion, but that's not how it's done.

File: sqrt.png (4KB, 801x63px) Image search: [Google]

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WTF do you do?

>>8895275
Well you know the two small triangles triangles are similar, so argue from there, I guess:

KP / 4 = 8 / KP

File: Screen Shot 2017-05-09 at 12.07.33 AM.png (35KB, 702x440px) Image search: [Google]

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How do they determine the vector from the matrix here? Please, I really need an explanation

>>8895413
By inspection desu. Eigenvalue 0 means we want v such that Av=0. A is simple enough that you can kind of work backwards by considering each row times v.

>>8895413
Your vector has 3 variables, and you have 3 equations:

0 v_11 + 2 v_12 + 2 v_13 = 0
2 v_11 + 1 v_12 + 0 v_13 = 0
2 v_11 + 0 v_12 + -1 v_13 = 0

Solve them and you get an eigen vector