1. Let A = 1 2 4 1 0 0 0-1 3 Answer the following a. Find the characteristic polynomial of A, and use it to find the eigenvalues. b. Find a basis for each eigenspace. c. Use your answer to diagonalize A as PDP-¹. Do not find P-1, instead verify by showing that AP = PD.
1. Let A = 1 2 4 1 0 0 0-1 3 Answer the following a. Find the characteristic polynomial of A, and use it to find the eigenvalues. b. Find a basis for each eigenspace. c. Use your answer to diagonalize A as PDP-¹. Do not find P-1, instead verify by showing that AP = PD.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Let A =
1
2 4 1
0
0
0-1 3
Answer the following
a. Find the characteristic polynomial of A, and use it to find the eigenvalues.
b. Find a basis for each eigenspace.
c. Use your answer to diagonalize A as PDP-¹. Do not find P-1, instead verify by showing that
AP = PD.
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