Let A = 4 2 07 020 0 1 4 (a) Write down char(A) and use it to find the eigenvalues of A. (b) Find the eigenvectors of A corresponding to each eigenvalue. (c) Find the eigenspace of A corresponding to each eigenvalue.

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 53E
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Let A =
4 2 07
020
0 1 4
(a) Write down char(A) and use it to find the eigenvalues of A.
(b) Find the eigenvectors of A corresponding to each eigenvalue.
(c) Find the eigenspace of A corresponding to each eigenvalue.
(d) Find nullity (A), nullity(A — 21), nullity(A - 4I) and nullity(A + I). Explain
your solution.
(e) Find the geometric multiplicity and algebraic multiplicity of each eigenvalue. Use
them to Explain why A is diagonalizable.
(f) Diagonalize A, which means finding P and D such that A = PDP-¹.
Transcribed Image Text:Let A = 4 2 07 020 0 1 4 (a) Write down char(A) and use it to find the eigenvalues of A. (b) Find the eigenvectors of A corresponding to each eigenvalue. (c) Find the eigenspace of A corresponding to each eigenvalue. (d) Find nullity (A), nullity(A — 21), nullity(A - 4I) and nullity(A + I). Explain your solution. (e) Find the geometric multiplicity and algebraic multiplicity of each eigenvalue. Use them to Explain why A is diagonalizable. (f) Diagonalize A, which means finding P and D such that A = PDP-¹.
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