Question: Concern the polynomial and an n n matrix C p called the companion matrix of p: Let p(t) = a 0 + a 1

Concern the polynomialp(t)= ao + at +...+ an-1t"-1 +t"and an n × n matrix Cp called the companion matrix of p:image


Let p(t) = a0 + a1t + a2t2 + t3, and let  be a zero of p. 


a. Write the companion matrix for p. 


b. Explain why λ3 = a0 - a1λ - a2λ2, and show that (1, λ, λ2) is an eigenvector of the companion matrix for p.

p(t)= ao + at +...+ an-1t"-1 +t"

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