(a) Let p(x) be a polynomial with coefficients in R, and let M abe the 3 x 3 matrix а 1 Ma := a 1 а Show that p(a) p'(a) p"(a) p(a) p'(a) p(a). p(Ma) (Hint: prove it first for monomials of the form x" by induction on n, and use the principle of linearity to prove this for all polynomials.) (b) Use this to determine the minimal polynomial of Ma.

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