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samuelr0750
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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.