Question: #12 please explain it 12. Let T be a linear operator on a finite-dimensional vector space V, and let be an eigenvalue of T with

#12 please explain it

12. Let T be a linear operator on a finite-dimensional vector space V, and let be an eigenvalue of T with corresponding eigenspace and generalized eigenspace Ex and Kx, respectively. Let U be an invertible linear opera- tor on V that commutes with T (i.e., TU = UT). Prove that U(Ex) = Ex and U(Kx) = Kx. Exercises 13 and 14 are concerned with direct sums of matrices, defined in Section 5.4 on page 318

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