Question: Q 1 Consider a 4 X 4 matrix A, which has four eigenvalues: A0 = 0, A1 : 11 A2 = 2, A3 : 3.

Q 1 Consider a 4 X 4 matrix A, which hasfour eigenvalues: A0 = 0, A1 : 11 A2 = 2, A3

Q 1 Consider a 4 X 4 matrix A, which has four eigenvalues: A0 = 0, A1 : 11 A2 = 2, A3 : 3. Assume that 136 is an eigenvector of A0, 171 is an eigenvector of A1, 113 is an eigenvector of A2 and 133' is an eigenvector of A3. (For each of the question parts, briey justify your answer and show your work step-by-step. Correct answers not supported by substantive explanations will receive no credit.) (d) (1 point) Explain why { vo, v1, v2, 13} is a linearly independent set. (e) (1 point) Are vi, v2 and v3 in Col(A)? (f) (1 point ) Find a basis for Col(A), if possible

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