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Solve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 1 3 Knowing that f (t) = (t – 1)²(t – 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P-AP is a diagonal matrix D. Give D

Solve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 1 3 Knowing that f (t) = (t – 1)²(t – 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P-AP is a diagonal matrix D. Give D

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 5EQ: In Exercises 1-6, show that vis an eigenvector of A and find the corresponding eigenvalue....
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Solve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 2 1 -2 2 3 -4 1 1 1 - Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P- AP is a diagonal matrix D. Give D
Transcribed Image Text:Solve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 2 1 -2 2 3 -4 1 1 1 - Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P- AP is a diagonal matrix D. Give D
3. Explain why as n goes to infinity. the entries of the vector A" 2 1 go to infinity, while the entries of A" -1 stay the same.
Transcribed Image Text:3. Explain why as n goes to infinity. the entries of the vector A" 2 1 go to infinity, while the entries of A" -1 stay the same.
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