-2 2-1 1 -1 1 0 1 1 -1 0 1 0 0 0 0 0 0 0 2 -2 2 -1 1 -1 0 0 0 0 7 -7 7 -7 7 -6 0 0 0 0 7 -7 7 -7 -7 7-6 0 5 5 -5 0 5 5 1

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2 2 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 2 2 2 1 1 1 0 0 0 0 7 7 7 7 7 6 0 0 0 0 7 7 7 7 7 7 6 0 5 5 5 0 5 5 1 1 (48.77 KiB) Viewed 20 times

-2 2-1 1 -1 1 0 1 1 -1 0 1 0 0 0 0 0 0 0 2 -2 2 -1 1 -1 0 0 0 0 7 -7 7 -7 7 -6 0 0 0 0 7 -7 7 -7 -7 7-6 0 5 5 -5 0 5 5 1. Let N 0 0 0 0 0 0 7 7 -7 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (a) Show N is nilpotent, and determine its index k. qoooo (b) Determine the ladder and refinement indices d and j of N. (c) Determine an explicit Jordan triangle associated with N, i.e., find J1 ,...,Jk such that A(N; J1, ..., Jk) is a Jordan triangle associated with N. (d) Write down the Jordan canonical form In of N. (e) Determine an invertible matrix V such that N =V INV-1.