For the matrix A in Exercise 33, use the CayleyHamilton Theorem to compute A2, A3, and A4 by expressing each as a linear combination of I and A.
In exercise 33
An important theorem in advanced linear algebra says that if cA (λ) is the characteristic polynomial of the matrix A, then cA (A) = 0 (in words, every matrix satisfies its characteristic equation). This is the celebrated Cayley-Hamilton Theorem, named after Arthur Cayley (1821 - 1895), pictured below, and Sir William Rowan Hamilton. Cayley proved this theorem in 1 858. Hamilton discovered it, independently, in his work on quaternions, a generalization of the complex numbers.