Proof that this is a a subspace

Question

My math is really getting rusty, I need some help on the following problem.

Proof that $y$ in $R^n$: $y = Xk$, where k in $R^m$, this is subspace of $R^m$

Is this in $R^m$ by default?

Answer 1

HINT

Recall that for a subspace all the following three properties must be satisfied:

$1) \,\vec{0} \in W$

$2) \,\vec{v}+\vec{w} \in W$

$3) \,\vec{cv}\to c \cdot \vec{v} \ ,c \in \mathbb{R}$

In that case $X$ is a n-by m matrix and it should be not difficult to check the properties for $y\in \mathbb{R^n}$.