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## Homework Statement

R(M) and C(M) are the row and column spaces of M.

Let A be an nxp matrix, and B be a bxq matrix.

Show that C(AB) = C(A) when the orthogonal complement of R(A) + C(B) = R^p (i.e. the orthogonal complement of R(A) and C(B) span R^p).

## Homework Equations

I know that the orthogonal complement of R(A) is the null spaceo f A.

I also know that C(X'X) = C(X') but that doesn't help

## The Attempt at a Solution

Not sure where to go... thanks.