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## Homework Statement

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

## Homework Equations

Q = [tex]\{\left v = \left( v1, v2, 0 \right) | v1,v2 \in R \right\}[/tex]

Q = [tex]\{\left v = \left( v1, 0, 0 \right) | v1 \in R \right\}[/tex]

Q = [tex]\{\left v = \left( v1, v2 \right) \in R2 | v1 = v2 + 1, v1,v2 \in R \right\}[/tex]

## 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.