Proving Subspace in R^3 with Fixed Matrix A: W={x \in R^{3} :Ax=[^{1}_{2}]}

[eyehategod]

Let A be a fixed 2x3 matrix. Prove that the set
$W={x \in R^{3} :Ax=[^{1}_{2}]}$ (2x1 matrix 1 on top 2 at the bottom)


what does the information after the ":" mean? is it a condition?
I don't understand this problem. Can anyone help me out?

 

[radou]

what does the information after the ":" mean? is it a condition?
I don't understand this problem. Can anyone help me out?

Yes, it is a condition. You're trying to prove if this set of vectors x such that the condition after ":" holds is a subspace of R^3, I guess? You didn't completely lay out the problem, btw.

 

[JasonRox]

Ok, this is how set notation works.

If I say...

A = { x : x e N }

Then that read... x is an element of A if x is an element N (the natural numbers). Hence, A = N, right? Do you agree?

Let's think of something a little harder...

A = { (x,y) : x + y = 1, and x,y e Z }

Z is all the integers including 0. So, what's in A? Well, all (x,y) are elements of A if x+y=1 and x,y element of Z. An example is (0,1) because 0+1 = 1 and 0 e Z and 1 e Z.

Anyways, now go back and re-read that question and state it correctly. And look for the Theorem on how to show a set is a subspace.