For each of the following statements, prove if it is true or give a counter example if it is false. 1. The inverse of an invertible lower triangular matrix is an upper triangular matrix. 2. The sum of an upper triangular matrix and a lower triangular matrix is a diagonal matrix. 3. Given an n x n matrix A and a constant k, det(kA) = k" det(A).

For each of the following statements, prove if it is true or give a counter example if it is false. 1. The inverse of an invertible lower triangular matrix is an upper triangular matrix. 2. The sum of an upper triangular matrix and a lower triangular matrix is a diagonal matrix. 3. Given an n x n matrix A and a constant k, det(kA) = k" det(A).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section: Chapter Questions

Problem 1RQ

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