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Let 042 327 1 -2 ON 0 0 0 -2 0 HOOO II A (a) Find the characteristic polynomial of A (b) Find all eigenvalues of A (c) For each eigenvalue λ of A, what is the algebraic and geometric multiplicities of X? (d) For each eigenvalue λ of A, find a basis for the eigenspace Ex(A). (e) Is A diagonalizable? If so, give an eigenbasis for A.

Let 042 327 1 -2 ON 0 0 0 -2 0 HOOO II A (a) Find the characteristic polynomial of A (b) Find all eigenvalues of A (c) For each eigenvalue λ of A, what is the algebraic and geometric multiplicities of X? (d) For each eigenvalue λ of A, find a basis for the eigenspace Ex(A). (e) Is A diagonalizable? If so, give an eigenbasis for A.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
Problem 9RQ
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Let 042 327 1 -2 ON 0 0 0 -2 0 HOOO II A (a) Find the characteristic polynomial of A (b) Find all eigenvalues of A (c) For each eigenvalue λ of A, what is the algebraic and geometric multiplicities of X? (d) For each eigenvalue λ of A, find a basis for the eigenspace Ex(A). (e) Is A diagonalizable? If so, give an eigenbasis for A.
Transcribed Image Text:Let 042 327 1 -2 ON 0 0 0 -2 0 HOOO II A (a) Find the characteristic polynomial of A (b) Find all eigenvalues of A (c) For each eigenvalue λ of A, what is the algebraic and geometric multiplicities of X? (d) For each eigenvalue λ of A, find a basis for the eigenspace Ex(A). (e) Is A diagonalizable? If so, give an eigenbasis for A.
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