A, P and D are n x n matrices. Check the true statements below: A. If A is diagonalizable, then A is invertible. B. A is diagonalizable if and only if A has n eigenvalues, counting multiplicities. C. If there exists a basis for R" consisting entirely of eigenvectors of A, then A is diagonalizable. D. A is diagonalizable if A = PDP-1 for some diagonal matrix D and some invertible matrix P. Note: You are in the Reduced Scoring Period: All additional work done counts 95% of the original.

A, P and D are n x n matrices. Check the true statements below: A. If A is diagonalizable, then A is invertible. B. A is diagonalizable if and only if A has n eigenvalues, counting multiplicities. C. If there exists a basis for R" consisting entirely of eigenvectors of A, then A is diagonalizable. D. A is diagonalizable if A = PDP-1 for some diagonal matrix D and some invertible matrix P. Note: You are in the Reduced Scoring Period: All additional work done counts 95% of the original.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 63EQ

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