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1. For each of the following matrices A, determine (i) if A is diagonalizable over R and (ii) if A is diagonalizable over C. When A is diagonalizable over C, find the eigenvalues, eigenvectors, and eigenbasis, and an invertible matrix P and diagonal matrix D such that P-AP = D. 3 -1 1 (A) A = 1 Го -1 1 (В) А — 0 -2 [2 0 2 1 (C) A = 1 0 2 O O O 2

1. For each of the following matrices A, determine (i) if A is diagonalizable over R and (ii) if A is diagonalizable over C. When A is diagonalizable over C, find the eigenvalues, eigenvectors, and eigenbasis, and an invertible matrix P and diagonal matrix D such that P-AP = D. 3 -1 1 (A) A = 1 Го -1 1 (В) А — 0 -2 [2 0 2 1 (C) A = 1 0 2 O O O 2

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. For each of the following matrices A, determine (i) if A is diagonalizable over R and (ii) if A is diagonalizable over C. When A is diagonalizable over C, find the eigenvalues, eigenvectors, and eigenbasis, and an invertible matrix P and diagonal matrix D such that P-AP = D. 3 -1 1] (A) A 1 1 ГО —1 0 (В) А - -2 2 Г2 1 01 0 2 1 0 2 (C) A =
Transcribed Image Text:1. For each of the following matrices A, determine (i) if A is diagonalizable over R and (ii) if A is diagonalizable over C. When A is diagonalizable over C, find the eigenvalues, eigenvectors, and eigenbasis, and an invertible matrix P and diagonal matrix D such that P-AP = D. 3 -1 1] (A) A 1 1 ГО —1 0 (В) А - -2 2 Г2 1 01 0 2 1 0 2 (C) A =
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