4 8 Marks Let A And B Be Two Matrices Whose Product Is Defined A Show That Row Ab C Row B Hint Start With Sh 1 (37.94 KiB) Viewed 35 times
(4) (8 marks) Let A and B be two matrices whose product is defined. (a) Show that row(AB) C row(B). (Hint, start with showing that rows of AB are linear combination of rows of B). (b) Use part (1) and transpose to show that col (AB) C col(A).
(c) Find an example to show that row space of AB needs not to be equal to row space of B. (d) Show that if A invertible then the equality holds, i.e. row(AB) = row(B) (Hint: Use (1) and B = A-¹(AB)) (e) Use (d) to give another proof for Theorem 3.20.
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