# Linear Algebra (Subspaces)

## Homework Statement

Okay, this is the last True/False question I will post.

True or False:
$$\text{The set of all solutions to the }m\times n\text{ homogeneous system of equations }Ax=0\text{ is a subspace of }\mathbb{R}^m.$$

None

## The Attempt at a Solution

I thought the answer was true, but it is actually false. I know that in order to qualify as a subspace, all linear combinations of the solutions must present a solution that remains in that subspace, but I wasn't sure how to justify my answer.

## Answers and Replies

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Try to find a counterexample

I guess there is the possibility of the trivial solution. Is this enough to say it is false?