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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Linear Algebra And Its Applications
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- In Exercises 19–22, evaluate the (4X4) determinants. Theorems 6–8 can be used to simplify the calculations.arrow_forwardIn Exercises 8–19, calculate the determinant of the given matrix. Use Theorem 3 to state whether the matrix is singular or nonsingulararrow_forwardIn Exercises 29–32, find the elementary row operation that trans- forms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
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