- #1

- 3

- 0

## Homework Statement

Let W = R3 be the set W = {(x,y,z)|z=y-2x}. Show that W is a subspace of R3

## Homework Equations

From the equations my teacher gave me I know that if W is to be a subspace it needs to follow:

1.) U,VεW then (U + V)εW,

2.)UεW and K(random constant)εW then KUεW

## The Attempt at a Solution

So I haven't really figured out how to attempt this problem but from what I know is that you need to assign U and V to something. From what Ive done so far I have U = (1,-2,-1) and V = (2,-4,-2). I got those numbers from the z=y-2x equation. Then U+V = (3,-6,-3), which I believe froms the first equation I gave.

Then I believe I pick a random constant for K, so ill choose 3. So 3U = (3,-6,-3) which proves the second equation.

Are these the proper steps to solving this problem?