# Linear algebra help: Subspaces

1. Feb 20, 2012

### epkid08

1. The problem statement, all variables and given/known data
Prove that C(AB) is a subset of C(A) for matrices A,B, where C denotes column space.

2. Relevant equations
C(AB) = {b \in \mathbbcode{R}^m: Ax=b is consistent}

3. The attempt at a solution
I don't really know where to start.

2. Feb 21, 2012

### vela

Staff Emeritus
What's the definition of a subset?

3. Feb 21, 2012

### Deveno

to make things easier suppose that A is mxn, and B is nxp. so AB is mxp.

now..hint: suppose u is in C(AB), which means that ABx = u, for some x in Rp.

can you think of some vector v in Rn, with Av = u?

(what mapping do we know for sure produces a vector in Rn?)