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(a) A is diagonalizable if A = PDP-¹for some matrix D and some invertible matr (b) If A is diagonalizable, then A has n distinct eigenvalues (c) If A is invertible, then A is diagonalizable (d) A factorization A = PDP-¹ is not unique. (e) If a is both diagonalizable and invertible, then A-¹ is diagonalizable and inve All of the above O None of the above Statements a, b, and d O Statements a, b, and e O Statements b, and e Statamants a O and a

(a) A is diagonalizable if A = PDP-¹for some matrix D and some invertible matr (b) If A is diagonalizable, then A has n distinct eigenvalues (c) If A is invertible, then A is diagonalizable (d) A factorization A = PDP-¹ is not unique. (e) If a is both diagonalizable and invertible, then A-¹ is diagonalizable and inve All of the above O None of the above Statements a, b, and d O Statements a, b, and e O Statements b, and e Statamants a O and a

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Which of the following statements is(are) if

A, P and D are n x n matrices. (a) A is diagonalizable if A = (b) If A is diagonalizable, then A has n distinct eigenvalues (c) If A is invertible, then A is diagonalizable (d) A factorization A = PDP-¹ is not unique. (e) If a is both diagonalizable and invertible, then A¯¹ is diagonalizable and invertible All of the above None of the above Statements a, b, and d Statements a, b, and e O Statements b, and e Statements a, c, and e Statements a, b, d and e PDP for some matrix D and some invertible matrix P
Transcribed Image Text:A, P and D are n x n matrices. (a) A is diagonalizable if A = (b) If A is diagonalizable, then A has n distinct eigenvalues (c) If A is invertible, then A is diagonalizable (d) A factorization A = PDP-¹ is not unique. (e) If a is both diagonalizable and invertible, then A¯¹ is diagonalizable and invertible All of the above None of the above Statements a, b, and d Statements a, b, and e O Statements b, and e Statements a, c, and e Statements a, b, d and e PDP for some matrix D and some invertible matrix P
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