(1) A scalar matrix A is an n x× n matrix such that for some real number r and all n × p matrices B, AB=rB. (a) Describe all scalar matrices. (b) Show that if A is a scalar matrix, then A must be as you described above. Hint: Consider AI.

(1) A scalar matrix A is an n x× n matrix such that for some real number r and all n × p matrices B, AB=rB. (a) Describe all scalar matrices. (b) Show that if A is a scalar matrix, then A must be as you described above. Hint: Consider AI.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 41EQ: In general, it is difficult to show that two matrices are similar. However, if two similar matrices...

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(1) A scalar matrix A is an n × n matrix such that for some real number r and all n × p matrices B,
AB = rB.
(a) Describe all scalar matrices.
(b) Show that if A is a scalar matrix, then A must be as you described above. Hint: Consider AI.

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