Let A be a diagonalizable matrix with characteristic polynomial p() = a1n + a2n1 + +an+1
Chapter 6, Problem 33(choose chapter or problem)
Let A be a diagonalizable matrix with characteristic polynomial p() = a1n + a2n1 + +an+1 (a) Show that if D is a diagonal matrix whose diagonal entries are the eigenvalues of A, then p(D) = a1Dn + a2Dn1 + +an+1 I = O (b) Show that p(A) = O. (c) Show that if an+1 _= 0, then A is nonsingular and A1 = q(A) for some polynomial q of degree less than n.
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