Question: Define T: R3 R3 by T(x) = Ax, where A is a 3 x 3 matrix with eigenvalues 5, 5, and -2. Does there

Define T: R3 → R3 by T(x) = Ax, where A is a 3 x 3 matrix with eigenvalues 5, 5, and -2. Does there exist a basis B for R3 such that the B-matrix for T is a diagonal matrix? Discuss.

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