E.S. nsider the following matrix: 1 1 0\ A=0 2 0 0 3 0 ➡blem E.3.a. Find the eigenvalue(s) and the eigenvector(s). oblem E.3.b. Is the matrix A diagonalizable? If so, what is the matrix P that diagon

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
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Problem E.3.
Consider the following matrix:
1 1 0
A=0 2 0
0 3
0
Problem E.3.a. Find the eigenvalue(s) and the eigenvector(s).
Problem E.3.b. Is the matrix A diagonalizable? If so, what is the matrix P that diagonalizes A?
Problem E.3.c. If the matrix A is diagonalizable, find the diagonal matrix D that is associated to A by calculating
D = P-¹AP. Show the work for finding P-¹ and for finding the matrix product P-¹AP.
Problem E.3.d. If the matrix A is diagonalizable, find the diagonal matrix D that is associated to A directly from
the eigenvalues found in problem E.3.a.
Transcribed Image Text:Problem E.3. Consider the following matrix: 1 1 0 A=0 2 0 0 3 0 Problem E.3.a. Find the eigenvalue(s) and the eigenvector(s). Problem E.3.b. Is the matrix A diagonalizable? If so, what is the matrix P that diagonalizes A? Problem E.3.c. If the matrix A is diagonalizable, find the diagonal matrix D that is associated to A by calculating D = P-¹AP. Show the work for finding P-¹ and for finding the matrix product P-¹AP. Problem E.3.d. If the matrix A is diagonalizable, find the diagonal matrix D that is associated to A directly from the eigenvalues found in problem E.3.a.
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