# Determining a subspace?

Hey, this isn't for homework per se, but if anyone could lend me a hand figuring this out I'd appreciate it a lot!

## Homework Statement

Determine whether Q is a subspace of R2/R3 in the following cases:

## Homework Equations

Q = $$\{\left v = \left( v1, v2, 0 \right) | v1,v2 \in R \right\}$$

Q = $$\{\left v = \left( v1, 0, 0 \right) | v1 \in R \right\}$$

Q = $$\{\left v = \left( v1, v2 \right) \in R2 | v1 = v2 + 1, v1,v2 \in R \right\}$$

## The Attempt at a Solution

I honestly am not sure where I'm meant to start here. I know there are 3 conditions where a subspace may be valid; when it's equal to zero, If X and Y are in U, then X+Y is also in U
and If X is in U then aX is in U for every real number a.

How exactly am I meant to go about applying those rules? If someone could set me off on the right track that'd be awesome.

## Answers and Replies

$$\{\left v = \left( v1, v2, 0 \right) | v1,v2 \in R \right\}$$

(0,0,0) is clearly in Q

Let x = (x1,x2,0) and y =(y1,y2,0) be vectors in Q

then x+y = (x1+y1, x2+y2, 0) is also in Q

and ax = a(x1,x2, 0) = (ax1, ax2, 0) is in Q

Mark44
Mentor
Hey, this isn't for homework per se, but if anyone could lend me a hand figuring this out I'd appreciate it a lot!

## Homework Statement

Determine whether Q is a subspace of R2/R3 in the following cases:

## Homework Equations

Q = $$\{\left v = \left( v1, v2, 0 \right) | v1,v2 \in R \right\}$$

Q = $$\{\left v = \left( v1, 0, 0 \right) | v1 \in R \right\}$$

Q = $$\{\left v = \left( v1, v2 \right) \in R2 | v1 = v2 + 1, v1,v2 \in R \right\}$$

## The Attempt at a Solution

I honestly am not sure where I'm meant to start here. I know there are 3 conditions where a subspace may be valid; when it's equal to zero, If X and Y are in U, then X+Y is also in U
and If X is in U then aX is in U for every real number a.
To correct your terminology, there are 3 conditions for verifying that a subset U of a vector space V is a subspace of that vector space. 1) Zero is an element of U. The other two are fine.
How exactly am I meant to go about applying those rules? If someone could set me off on the right track that'd be awesome.

See RandomVariable's reply.

Cool, thanks very much guys. Makes sense now!