Linear algebra help: Subspaces

[epkid08]

Homework Statement

Prove that C(AB) is a subset of C(A) for matrices A,B, where C denotes column space.

Homework Equations

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

The Attempt at a Solution

I don't really know where to start.

 

[vela]

What's the definition of a subset?

 

[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 R^p.

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

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