-9 -3 -15 0 -7 0 -6 Let A = where c is an unknown scalar. 0 7 2 13 0 4 0 3 (a) Without using software, show that p₁(A) = (\—c)(\+3)(A+1)(\−2) is the characteristic polynomial of A. (b) Determine the values of c for which the matrix A is not diagonalizable. Use of software is allowed on this part.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 43E
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C
-3 -15
0
-7
0 -6
5.
Let A =
where c is an unknown scalar.
C
"
0
7
2
13
0
4
0 3
(a) Without using software, show that pÃ(\) = (\—c)(\+3)(\+1)(\−2) is the characteristic
A
polynomial of A.
(b) Determine the values of c for which the matrix A is not diagonalizable. Use of software
is allowed on this part.
Transcribed Image Text:C -3 -15 0 -7 0 -6 5. Let A = where c is an unknown scalar. C " 0 7 2 13 0 4 0 3 (a) Without using software, show that pÃ(\) = (\—c)(\+3)(\+1)(\−2) is the characteristic A polynomial of A. (b) Determine the values of c for which the matrix A is not diagonalizable. Use of software is allowed on this part.
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