Suppose that a matrix A has the following eigenvalues and eigenvectors: T • λ=−1haseigenvectorx=[1, 2, 3] . T • λ=2haseigenvectory=[−1, 0, 2] . T • λ=3haseigenvectorz=[0, 2, 1] . (i) Write the vector v = [1, 10, 11]T as a linear combination of x, y, and z. (ii) Calculate Av using your solution from Part (i).

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Q: Suppose the 3 × 3 matrix A has eigenvalues λ1 = −6, λ2 = −2, and λ3 = 5.

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Q: (b) Find a complete orthonormal set of eigenvectors {v1, v2, V3}, where v; is an vector for A;.…

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Q: What is the eigenvalue of the operator T, given by T(x) = 3x + 2, for the vector x = [1, 2]?

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A: See solution below.

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