Let A be a 5 x 5 matrix with eigenvalues A1 = 0, A2 = 13 = 1, d4 = -2, A5 = –1. %3D (a) What is the algebraic multiplicity for each eigenvalue of A? (b) Suppose A ~ B. Calculate the eigenvalues of B² + 3I, where I, is the 5 × 5 identi matrix.

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
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Let A be a 5 x 5 matrix with eigenvalues A1 = 0, A2 = 13 = 1, d4 = -2, A5 = –1.
%3D
(a) What is the algebraic multiplicity for each eigenvalue of A?
(b) Suppose A ~ B. Calculate the eigenvalues of B2 + 3I,, where I, is the 5 × 5 identity
matrix.
Transcribed Image Text:Let A be a 5 x 5 matrix with eigenvalues A1 = 0, A2 = 13 = 1, d4 = -2, A5 = –1. %3D (a) What is the algebraic multiplicity for each eigenvalue of A? (b) Suppose A ~ B. Calculate the eigenvalues of B2 + 3I,, where I, is the 5 × 5 identity matrix.
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