6. Consider the matrices A= = 2 6 -15 1 1 12 -5; B -6 = 5 -7 3 6 -9 4 (1) Compute the characteristic polynomial of A and B; (2) Compute the Jordan canonical form of A and B; (3) Compute A-1 using Cayley-Hamilton Theorem.

6. Consider the matrices A= = 2 6 -15 1 1 12 -5; B -6 = 5 -7 3 6 -9 4 (1) Compute the characteristic polynomial of A and B; (2) Compute the Jordan canonical form of A and B; (3) Compute A-1 using Cayley-Hamilton Theorem.

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 41E

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Question

6. Consider the matrices
A
=
1
1
2
-15
-5; B
-6
=
-5 2
5 -7 3
6-9 4
(1) Compute the characteristic polynomial of A and B;
(2) Compute the Jordan canonical form of A and B;
(3) Compute A-¹ using Cayley-Hamilton Theorem.

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Step 2: Characteristic polynomial of B

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Step 3: Minimal polynomial of A and B

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Step 4: Jordan canonical forms

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