Prove that if both products AB and BA are defined, then AB and BA are square matrices. Assume that A is an m xn matrix and B is a p xq matrix. Because AB is defined, you have that ---Select-- v and AB is a(n) -Select-- v matrix. Because BA is defined, you have that -Select-- v and so AB is an --Select- v square matrix. Likewise, because BA is defined, --Select- v and BA is a(n) ---Select--- v matrix. Because AB is defined, you have -Select-- v Therefore, BA is an-Select-v square matrix.

Prove that if both products AB and BA are defined, then AB and BA are square matrices. Assume that A is an m xn matrix and B is a p xq matrix. Because AB is defined, you have that ---Select-- v and AB is a(n) -Select-- v matrix. Because BA is defined, you have that -Select-- v and so AB is an --Select- v square matrix. Likewise, because BA is defined, --Select- v and BA is a(n) ---Select--- v matrix. Because AB is defined, you have -Select-- v Therefore, BA is an-Select-v square matrix.

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...

See similar textbooks