Question: 3. Given A E R17x17. Let P = [pilp2) . . .[p17] be invertible such that AP = PJ where J is the Jordan canonical

3. Given A E R17x17. Let P = [pilp2) . . .[p17] be invertible such that AP = PJ where J is the Jordan canonical form as follows 3 3 5 7 -JH 7 7 7 7 -JH (a) Among p1, p2, . .. ,P17, which is (are) eigenvector(s)? (b) Find ind(5) and ind(7). (c) Find algebraic and geometric multiplicities for 1 = 3, 7. (d) Is there any semi-simple eigenvalue for J? Why? (e) Find dep(p5) and dep(P13)
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