Question: AE 3.1 For the n x n matrix A = 0 -do -(12 -an-2 -an-1 a. Use mathematical induction on n to show that the

AE 3.1 For the n x n matrix A = 0 -do -(12 -an-2 -an-1 a. Use mathematical induction on n to show that the character- istic polynomial of A is 2" + an-12" -+ an-22"-2 + ... + azk + aid + do b. If ; is an eigenvalue of A, show that a corresponding eigen- vector is given by c. Show that the geometric multiplicity of each distinct eigen- value is one

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