Let T be the linear operator on MnXn(i) defined by T(A) = A1 . (a) Show that 1 are the
Chapter 5, Problem 17(choose chapter or problem)
Let T be the linear operator on MnXn(i?) defined by T(A) = A1 . (a) Show that 1 are the only eigenvalues of T. (b) Describe the eigenvectors corresponding to each eigenvalue of T. (c) Find an ordered basis 0 for M2x2(Z?) such that [T]/3 is a diagonal matrix. (d) Find an ordered basis 0 for Mnx(R) such that [T]p is a diagonal matrix for n > 2.
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