Consider the matrix, A = -3 0 T 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-¹ AS = D is diagonal. Also write down the r D explicitly. -2 -1 -17

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Consider the matrix,
-2
-1 -17)
A = -3
0
13
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-¹ AS = D is diagonal. Also write down the matrix
D explicitly.
Transcribed Image Text:Consider the matrix, -2 -1 -17) A = -3 0 13 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-¹ AS = D is diagonal. Also write down the matrix D explicitly.
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