Exercises 19–23 concern the polynomial
p(t) = a0 + a1t + … + an−1tn−1 + tn
and an n × n matrix Cp called the companion matrix of p:
Cp =
22. Let p(t) = a0 + a1t + a2t2 + t3, and let λ 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.
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