1 -1 1. Let A = 1 3 -3 1 a. Find the characteristic polynomial of A. b. Find the eigenvalues of A. c. Determine the geometric and algebraic multiplicities of its eigenvalues. d. Is A diagonalizable? Explain your answer. e. If A is diagonalizable, find a nonsingular matrix P such that P-1AP is diagonal. f. Use the Hamilton-Cayley Theorem to find the inverse of A.
1 -1 1. Let A = 1 3 -3 1 a. Find the characteristic polynomial of A. b. Find the eigenvalues of A. c. Determine the geometric and algebraic multiplicities of its eigenvalues. d. Is A diagonalizable? Explain your answer. e. If A is diagonalizable, find a nonsingular matrix P such that P-1AP is diagonal. f. Use the Hamilton-Cayley Theorem to find the inverse of A.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 12EQ
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