Verify the Cayley-Hamilton Theorem for A The Cayley-Hamilton Theorem can be used to
Chapter 4, Problem 4.3.34(choose chapter or problem)
Verify the Cayley-Hamilton Theorem for A The Cayley-Hamilton Theorem can be used to calculate powers and inverses of matrices. For example, if A is a 2 2 matrix with characteristic polynomial cA(l) l2 al b, then A2 aA bI O, so and It is easy to see that by continuing in this fashion we can express any positive power of A as a linear combination of I and A. From A2 aA bI O, we also obtain A(A aI) bI, so provided b 0. 3
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