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 + C1A + c2A? +...

Extracted text: 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 + C1A + c2A? + A3 = 0, so A3 = - c2A? - c1A – CoI Multiplying through by A yields A4 = - COA - CA? - C2A³, which expresses A4 in terms of A3, A? and A. Use this procedure to calculate A³ and A4 for 1 0 A = |0 0 1 1 -7 7 A3 is


Extracted text: A4 is