Let T E ACUR"). {a} Suppose n = 5 and that 8 is an eigenvalue of T whose associated eigeusparre E3 is zit-dimensional. Prove that either T 71' or T...

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3. Let T E ACUR“). {a} Suppose n = 5 and that 8 is an eigenvalue of T whose associated eigeusparre E3 is zit-dimensional.Prove that either T — 71' or T — Q! is invertible. (b) Suppose n = 3 and that 7 and Q are the only eigenvalues of T. Furthermore, suppose that dim(E7) =diJI1(Eg) = 1. Prove that there exists (my, .3) E R3 such that T(3:,y, z) = (fi+ 8:51 VIE + By, VE+ 83). {e} Suppose a = 2 and that T4 = —I. Give an example of such a T.