Consider the matrix, -2 -1 -17 A = -3 0 π 0 0 3 a) Compute the characteristic polynomial and the eigenvalues of A. b) Why is A diagonalizable?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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Consider the matrix,
-2 -1 -17
A =
-3
0
π
0
0
3
a) Compute the characteristic polynomial and the eigenvalues of A.
b) Why is A diagonalizable?
c) Explicitly compute an invertible matrix, S, so that S−¹AS = D is diagonal. Also write down the matrix D
explicitly.
Transcribed Image Text:Consider the matrix, -2 -1 -17 A = -3 0 π 0 0 3 a) Compute the characteristic polynomial and the eigenvalues of A. b) Why is A diagonalizable? c) Explicitly compute an invertible matrix, S, so that S−¹AS = D is diagonal. Also write down the matrix D explicitly.
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