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72 8 1).' A = 0-3 0-3,A=-1 -10 -2 -11 a. Find the characteristic equation and show that the solutions of the characteristic are the given eigenvalues. b. For each eigenvalue, find a basis for the eigenspace. What is the dimension of each eigenspace? c. Can A be diagonalizable? Why? If yes, write P and D and on the diagonal of D, list the eigenvalues from smallest to largest. (Note that the more negative, the smaller the value.) d. Find the inverse of P using an adjucate matrix.

72 8 1).' A = 0-3 0-3,A=-1 -10 -2 -11 a. Find the characteristic equation and show that the solutions of the characteristic are the given eigenvalues. b. For each eigenvalue, find a basis for the eigenspace. What is the dimension of each eigenspace? c. Can A be diagonalizable? Why? If yes, write P and D and on the diagonal of D, list the eigenvalues from smallest to largest. (Note that the more negative, the smaller the value.) d. Find the inverse of P using an adjucate matrix.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 1BEXP
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72 8 1).' A = 0-3 0-3,A=-1 -10 -2 -11 a. Find the characteristic equation and show that the solutions of the characteristic are the given eigenvalues. b. For each eigenvalue, find a basis for the eigenspace. What is the dimension of each eigenspace? c. Can A be diagonalizable? Why? If yes, write P and D and on the diagonal of D, list the eigenvalues from smallest to largest. (Note that the more negative, the smaller the value.) d. Find the inverse of P using an adjucate matrix.
Transcribed Image Text:72 8 1).' A = 0-3 0-3,A=-1 -10 -2 -11 a. Find the characteristic equation and show that the solutions of the characteristic are the given eigenvalues. b. For each eigenvalue, find a basis for the eigenspace. What is the dimension of each eigenspace? c. Can A be diagonalizable? Why? If yes, write P and D and on the diagonal of D, list the eigenvalues from smallest to largest. (Note that the more negative, the smaller the value.) d. Find the inverse of P using an adjucate matrix.
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