is there something i'm missing in my textbook? why the hell

does Z2 not denote a field of mod 2, in which case you would get (y + 1) mod 2 = 0
?

>>7775561

Isn't Z_{2} the quotient group Z/2Z, so that 1=-1 (mod 2)?

>>7775582
this
add the two equations together as stated in the solution

2x + y + 2z = 1

2x = 0 in Z2
2z = 0 in Z2
Therefore you're left with y=1

>>7775587
Given that the first equation is y + (x + z) = 0

and the second is x + z = 1

then why isn't the first equation, when substituted, y + 1 = 0

and then why isn't y = -1?

>>7775590
Probably because the integer -1 is not an element of this field. Look again to the way they have defined it. This is consistent with the fact that the text shows there are only 2 solutions, and not infinite ones.

>>7775590
y+1=0 is correct

that means you have to look for the inverse element of 1 for the operation + in Z2

and that is the element 1

there is no such thing as substraction, only addition

you can also start from y+1=0, and add 1
y+0 = 1

>>7775599
>>7775613

You guys are right. I misunderstood the question.

Is this a troll post? The only real number solution here is y = -1

If you input the numbers from that 'solution', you get 2 for both equations which are obviously false. The actual solution is x = 1, y = -1, z = 0.

do not respond to that last post

>>7775642
>begins troll post by asking if another post is a troll post
I see you there, troll

>>7775642
>>7775656
>>7775646

huehuehue, ok I solved it for realsies. I think this is beyond what OP is studying but here is the real answer:

x = -t
y = -1
z = t + 1

>>7775682

That screenshot is still wrong as fuck though. The proposed points do not fit the first equation at all.

>>7775721
they do...

>>7775725

Really? 1 + 1 + 0 = 2, 0 + 1 + 1 = 2. That shit is nonsense. They only fit the second equation but not the first. The other answer:

x = -t
y = -1
z = t + 1

is correct.

>>7775732
there is no 2 in [math]\mathbb{Z}_2[/math], only the classes 0 and 1

Oh shit, I'm dumb, I didnt even read that shit.. That is what booze does to you I guess.

>>7775721
You are a fucking idiot.

>>7775768

shhhh don't tell them that.

>>7775768
Well, technically 2 is in [0].

Ive never seen before a math problem of this kind, what is the field?

>>7775934
Linear Algebra

>>7775934
[math]\mathbb F_2 [/math] :^)