Please show all the steps 6. Prove that if M is an n x n matrix that has a "block form"A BM = (42)where the sizes of A, B, C are k×k, k× (n − k) and (n − k) × (n − k) respectively, thendet (M) = det (A) det (C).

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Answered: 6. Prove that I M is an n x n matrix…

6. Prove that I M is an n x n matrix that has a DIOCK Iorm A B (18) where the sizes of A, B, C are k x k, k× (n − k) and (n − k) × (n − k) respectively, then det (M) = det (A) det(C). M =

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 63EQ

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Question

Please show all the steps

6. Prove that if M is an n x n matrix that has a "block form"
A B
M = (42)
where the sizes of A, B, C are k×k, k× (n − k) and (n − k) × (n − k) respectively, then
det (M) = det (A) det (C).

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