Question 18 Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A= PDP-1 [200] A = 120 [10-1] 201 P= 2 2 0.D=121 11 1 [100] [210] P= 2 2 0.D-020 011 002 O Not diagonalizable 002 -101 12 1 P=021.D-020 200 002

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 8AEXP
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Question 18
Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A- PDP-1
[200]
A = 120
O [10-1]
O
201
P= 2 2 0.D=121
11
1
[100]
[2 1 0
P= 2 2 0.D=0 20
011
002
O Not diagonalizable
O
002
12 1
200
P= 02 1.D-020
-101
Question 19
002
Define T: R² R2 by T(x) = Ax, where A is the matrix defined below. Find the requested basis B for R2 and the corres
matrix for T.
Transcribed Image Text:Question 18 Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A- PDP-1 [200] A = 120 O [10-1] O 201 P= 2 2 0.D=121 11 1 [100] [2 1 0 P= 2 2 0.D=0 20 011 002 O Not diagonalizable O 002 12 1 200 P= 02 1.D-020 -101 Question 19 002 Define T: R² R2 by T(x) = Ax, where A is the matrix defined below. Find the requested basis B for R2 and the corres matrix for T.
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