Recent content by samuelr0750

I"m sorry, i meant A is nxp and B is p xq.

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...

Homework Statement Let U be the span of k vectors, {u1, ... ,uk} and Pu be the orthogonal projection onto U. Let V be the span of l vectors, {v1, ... vl} and Pv be the orthogonal projection onto V. Let X be the span of {u1, ..., uk, v1, ... vl} and Px be the orthogonal projection onto X...