The Cayley-Hamilton Theorem provides a method for calculating powers of a matrix. For example, if A is a 3 x 3 matrix with the characteristic equation Co + c11 + c21² + 13 = 0 then coI + c,A + cA? + A3 = 0, so A3 = - CA2 - gA - coI Multiplying through by A yields A4 = - CoA - C,A² – c2A³, which expresses A4 in terms of A3, A² and A. Use this procedure to calculate A3 and A4 for 0. 1 0 0 1 |1 -7 7 A =|0

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