Chapter 5, Supplementary Exercises, Question 10 The Cayley-Hamilton Theorem provides a method for calculating powers of a matrix. For example, if A is a 3x 3 matrix with the characteristic equation...

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Extracted text: Chapter 5, Supplementary Exercises, Question 10 The Cayley-Hamilton Theorem provides a method for calculating powers of a matrix. For example, if A is a 3x 3 matrix with the characteristic equation then cl + c,A + c,A? A-0, so A -A-A- God Multiplying through by A yields AcA - cA? - cA, which expresses A in terms of A, A and A. Use this procedure to calculate A and Af for 1 0] A-0 0 1 -2 2