What is the solution space and subspace of a given matrix?

[Aerosion]

Homework Statement

Let A =

[2 -1 9]
[1 0 5]
[0 1 1]

Find solution space W and prove that W is a subspace of R^3.

Homework Equations

The Attempt at a Solution

rref=
[1 0 5]
[0 1 1]
[0 0 0]

So I know the row-echeleon form, which is what I suppose is the solution space. But how do you prove that it's a subspace of R^3? Using the vector space axioms? How do you use those on this kind of matrix?

 

[cristo]

The matrix isn't the solution space. The solution space is the set of vectors x such that Ax=0.