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A = [-¹/₂ 4 a. is the matrix A diagonalizable or not (and why)? b. find a nonsingular matrix P such that PIAP is diagonal (and deduce the diagonal form of A) Consider the following matrix in M₂x2²

A = [-¹/₂ 4 a. is the matrix A diagonalizable or not (and why)? b. find a nonsingular matrix P such that PIAP is diagonal (and deduce the diagonal form of A) Consider the following matrix in M₂x2²

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 15CR: For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of...
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11 Consider the following matrix in M₂x2² A = [¹21] a. is the matrix A diagonalizable or not (and why)? b. find a nonsingular matrix P such that P¹AP is diagonal (and deduce the diagonal form of A)
Transcribed Image Text:11 Consider the following matrix in M₂x2² A = [¹21] a. is the matrix A diagonalizable or not (and why)? b. find a nonsingular matrix P such that P¹AP is diagonal (and deduce the diagonal form of A)
Ex 1: [102] Consider the following matrix in M3x3 B 0 3 0 [20 a- show that A₁ = -1 and X₂ = 3 are the eigenvalues of B b- evaluate the eigenvectors associated to the found eigenvalues. C- deduce the dimensions of the corresponding eigenspaces.
Transcribed Image Text:Ex 1: [102] Consider the following matrix in M3x3 B 0 3 0 [20 a- show that A₁ = -1 and X₂ = 3 are the eigenvalues of B b- evaluate the eigenvectors associated to the found eigenvalues. C- deduce the dimensions of the corresponding eigenspaces.
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