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.
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)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0126b65b-66a1-4930-86a7-96f79222b7bf%2Fb20755b9-52ed-443b-bf12-d69fc3feb24a%2Fjql50ro_processed.jpeg&w=3840&q=75)
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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