Consider a 5 x 5 matrix A with two distinct eigenvalues, X\ and A.2, with geometric

Chapter 7, Problem 67

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Consider a 5 x 5 matrix A with two distinct eigenvalues, X\ and A.2, with geometric multiplicities 3 and 2, respectively. What is the dimension of the linear space of all 5 x 5 matrices S such that AS = SD, where D is the diagonal matrix with the diagonal entries A j, X\, Ai, ^2, A2?

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