I'm not sure how to do this. . . .

Prove that, for any m x n matrix A and any n x p matrix B, the column space of AB is contained in the column space of A.

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- Nov 8th 2006, 04:01 PMTreeMoneyColumn Space
I'm not sure how to do this. . . .

Prove that, for any m x n matrix A and any n x p matrix B, the column space of AB is contained in the column space of A. - Nov 9th 2006, 03:36 PMBubbleBrain_103
Here's a hint:

If we think of any (m x n) matrix M as a linear transformation from R^n to R^m, then the column space of M is precisely the image of M... that is, if I take a column vector v in R^n, then the vector Mv in R^m always lies in the column space of M.