Problem 3 §7.2, Exercise 4. Consider the matrix -1 1 1 -1 1 -1 A = 1 (a) Verify that the characteristic polynomial of A is pa(A) = (X – 1)(A+2)². (b) Show that (1, 1, 1) is an eigenvector of A corresponding to A = 1. (c) Show that (1, 1, 1) is orthogonal to every eigenvector of A corresponding to the eigenvalue A= -2.

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