The Cayley-Hamilton theorem states that every matrix must satisfy its characteristic polyn...

The Cayley-Hamilton theorem states that every matrix must satisfy its characteristic polynomial pA. For example, the characteristic polynomial of

is pA(λ) = λ3 − 6λ2 + 11λ − 6. The following commands will verify that pA(A) = A3 − 6A2 + 11A — 6I = 0.

In Exercises, verify the Cayley-Hamilton theorem for the given matrix. Note: You may also want to investigate the polyvalm command.