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- Let p(t) = t5 - 6tª + 6t3 – 6t² + 5t. a) Factorise p(t) as a product of degree 1 polynomials. b) Give an example of a matrix with characteristic polynomial p(t). That is, find a matrix A such that PA(t) = p(t). c) Give an example of a degree 3 polynomial q(t) with real coefficients that has two imaginary roots. For the polynomial q(t) you find, give a matrix that has characteristic polynomial q(t).

- Let p(t) = t5 - 6tª + 6t3 – 6t² + 5t. a) Factorise p(t) as a product of degree 1 polynomials. b) Give an example of a matrix with characteristic polynomial p(t). That is, find a matrix A such that PA(t) = p(t). c) Give an example of a degree 3 polynomial q(t) with real coefficients that has two imaginary roots. For the polynomial q(t) you find, give a matrix that has characteristic polynomial q(t).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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3. Let p(t) = t5 – 6t4 + 6t3 – 6t² + 5t. a) Factorise p(t) as a product of degree 1 polynomials. b) Give an example of a matrix with characteristic polynomial p(t). That is, find a matrix A such that PA(t) = p(t). c) Give an example of a degree 3 polynomial q(t) with real coefficients that has two imaginary roots. For the polynomial q(t) you find, give a matrix that has characteristic polynomial q(t).
Transcribed Image Text:3. Let p(t) = t5 – 6t4 + 6t3 – 6t² + 5t. a) Factorise p(t) as a product of degree 1 polynomials. b) Give an example of a matrix with characteristic polynomial p(t). That is, find a matrix A such that PA(t) = p(t). c) Give an example of a degree 3 polynomial q(t) with real coefficients that has two imaginary roots. For the polynomial q(t) you find, give a matrix that has characteristic polynomial q(t).
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