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Let A = 4 000 0400 0213 0504 Find the characteristic polynomial X(t) of A. Use the Cayley-Hamilton Theorem to write A4 as an expression of A³, A², A and 14. Use the Cayley-Hamilton Theorem to write A-¹ as an expression in terms of A³, A2, A and I4.

Let A = 4 000 0400 0213 0504 Find the characteristic polynomial X(t) of A. Use the Cayley-Hamilton Theorem to write A4 as an expression of A³, A², A and 14. Use the Cayley-Hamilton Theorem to write A-¹ as an expression in terms of A³, A2, A and I4.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 7E
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Let A = 4 0 0 0 0400 0213 0504 Find the characteristic polynomial X(t) of A. Use the Cayley-Hamilton Theorem to write A4 as an expression of A³, A², A and I₁. Use the Cayley-Hamilton Theorem to write A-¹ as an expression in terms of A³, A2, A and I4.
Transcribed Image Text:Let A = 4 0 0 0 0400 0213 0504 Find the characteristic polynomial X(t) of A. Use the Cayley-Hamilton Theorem to write A4 as an expression of A³, A², A and I₁. Use the Cayley-Hamilton Theorem to write A-¹ as an expression in terms of A³, A2, A and I4.
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