Characteristic Polynomial Let be a matrix and define (a)
Chapter 7, Problem 7.1.1.162(choose chapter or problem)
Characteristic Polynomial Let \(A=\left[a_{i j}\right]\) be a \(2 \times 2\) matrix and define \(f(x)=\operatorname{det}\left(x I_{2}-A\right)\).
(a) Expand the determinant to show that \(f(x)\) is a polynomial of degree 2. (The characteristic polynomial of A)
(b) How is the constant term of \(f(x)\) related to det A?
(c) How is the coefficient of x related to A?
(d) Prove that \(f(A)=0\).
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