‒‒‒‒TATIAHN ? ? ? ? ? Are the following statements true or false for a square matrix A? 1. A matrix A is singular if and only if 0 is an eigenvalue of A. 2. An n x n matrix A is diagonalizable if A has n linearly independent eigenvectors. 3. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. 4. If A is invertible, then A is diagonalizable. 5. The sum of two eigenvectors of a matrix is always an eigenvector.

‒‒‒‒TATIAHN ? ? ? ? ? Are the following statements true or false for a square matrix A? 1. A matrix A is singular if and only if 0 is an eigenvalue of A. 2. An n x n matrix A is diagonalizable if A has n linearly independent eigenvectors. 3. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy. 4. If A is invertible, then A is diagonalizable. 5. The sum of two eigenvectors of a matrix is always an eigenvector.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section: Chapter Questions

Problem 17RQ

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