Question: Let A be an m x n matrix, B an n x r matrix, and C = AB. Show that (a) N(B) is a subspace

Let A be an m x n matrix, B an n x r matrix, and C = AB. Show that
(a) N(B) is a subspace of N(C).
(b) N(C)⊥- is a subspace of N(B)⊥ and, consequently, R(CT) is a subspace of R(BT).

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a If x NB then Cx ABx A0 0 Thus x NC and it follows ... View full answer

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