Question:

Let A and B be mxn matrices and let S be the set of all x in R^n such that Ax = Bx. Show that S is a subspace of R^n.

My approach:

So i know that there are 3 properties for H to be a subspace in R^n.

1) the zero vector is in H

2) for each u and v in H, the sum u+v is in H

3) for each u in H and each scalar c, the vector cu is in H

So im confused on how i would go abouts proving this?

Would i take property 3 and multiply Ax=BX by a scalar?