Let A be a k k matrix and let B be an (n k) (n k) matrix. Let E = Ik O O B , F = A O O

Chapter 2, Problem 18

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Let A be a k k matrix and let B be an (n k) (n k) matrix. Let E = Ik O O B , F = A O O Ink , C = A O O B where Ik and Ink are the k k and (n k) (n k) identity matrices. (a) Show that det(E) = det(B). (b) Show that det(F) = det(A). (c) Show that det(C) = det(A) det(B). 1

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