16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 4.2.1

Polynomials

Mathematics — Linear Algebra · polynomial-evaluation-matrix

Problem

Let FF be a subfield of the complex numbers and let AA be the following 2×22 \times 2 matrix over FF A=[21−13].A = \begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix}. For each of the following polynomials ff over FF, compute f(A)f(A). ((a)) f=x2−x+2f = x^2 - x + 2; ((b)) f=x3−1f = x^3 - 1; ((c)) f=x2−5x+7f = x^2 - 5x + 7.

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