Dumbass here. I don't know where else to turn. I'm

>>7941480
Ok, so imagine a 1 dimensional space take the Real number line for instance. You want to describe the position of something that line. How many real numbers would you need to describe the position?

>>7941490
1 real number

>>7941480
So what it is about span or linear independence you don't get?

The intuition should be very easy to get if you approach it geometrically. Have a look here.
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/

>>7941495
Alright, now imagine a plane, or a 2 dimensional space. How many numbers do you need to describe the position of a point?

>>7941503
2

>>7941499
Dude just look at my picture. Where the fuck did they get that combination of c values? It isnt easy at all and if I can't understand this, then I can't learn basis

>>7941503
>inb4 3

>>7941503

>How many numbers do you need to describe the position of a point?

One, such as 2+3i.

>>7941507
Ok, so those two numbers you need to describe a point can form something called a 'vector.' Now, suppose you want to describe the position of a point in the same plane that isn't colinear with the vector you have. You are going to need another vector that isn't colinear with your existing vector to describe the position of that point. A linear combination of those two vectors would be sufficient to describe the points position. In fact you could describe ANY points position with those two vectors. Those two vector form a basis of the vector space. For a vector space of dimension N you need N linearly independent vectors to space the vector space.

Linear independence is essentially a fancy way of saying "not colinear."

>>7941517
>Complex space requires linear combination of two basis vectors
ya blew it.

>>7941507
Dude, just do Gauss Jordan. If you get an identity matrix BINGO it spans and everything is linearly independent.

File: 1409929305970.png (290KB, 498x341px) Image search: [Google]

290KB, 498x341px

>>7941517
This poster trying to charge his lap top

>>7941522
>In fact you could describe ANY points position with those two vector

that doesnt make sense. If two vectors aren't co-linear then tthey only interest at one point so how the hell can you describe any point when there's only one point invovled

>>7941480
ayy I know the book you're reading

>>7941507
It even says in your picture how they got them.

If you don't understand the solution, find the similar problem for two dimensional vectors. Draw them. Understand what vector addition is in that graph, understand what multiplying a vector by a scalar is.

Like, I have the vector (3,2).
S= { (0,1), (1,0) }

Can you express the vector (3,2) as a linear combination of the vectors in S?

>>7941563
any idea what the hell they're doing right below that solution word in blue bold? The one with C1+c3?

I can't replicate what they did

>>7941568
>Can you express the vector (3,2) as a linear combination of the vectors in S?

Obviously, 2v1 + 3v2

>>7941573
>>7941571
They are writing down the problem you just solved for two dimensional vectors.

Summing the vectors, multiplying each by a constant. The first entry of the resulting vector is c1*1 + c2*0 + c3*-1. It needs to equal 1.

etc

>>7941584
just nevermind. I figured out that all they did was make the vectors vertical. Not going to bother with asinine, complicated, tedious axioms I wont need to do the problems

>>7941517
>implying C isn't merely R^2 with well-defined multiplication

>>7941548
Simply by scaling the two vectors through scalar multiplication. consider the vectors:
(1,0) and (0,1)
I say that by multiplying through each of the entries by a scalar it is possible to describe each point in the Real plane.

>>7941599
Anon you will be in for a much more pleasant, meaningful, and simple experience if you learn the axioms and discover what they mean for yourself. If you go on to take an introductory course in differential equations you will be saving yourself a world of hurt.