Question

degree of the polynomial p (t) = 3t square -5​

Answer 1

Step-by-step explanation:

Let p(t) = 4 + 3t + 2t^2 + t^3, a polynomial of degree 3 in t. For any n x n matrix A, we define the square matrix p(A) by replacing t with A, specifically: p(A) = 4In + 3A + 2A^2 + A^3 . (a) Compute p(A) when A = [0 -1 1 0]. (b) Prove that if lambda is an eigenvalue of A, then p(lambda) is an eigenvalue of p(A). (c) Prove that if A is diagonalizable, then p(A) is also diagonalizable.