Question: Q 1 Consider a 3 x 3 matrix A, which has three eigenvalues, A0 = 0, A1 = 1, A2 = 2. Assume that 176

Q 1 Consider a 3 x 3 matrix A, which has three eigenvalues, A0 = 0, A1 = 1, A2 = 2. Assume that 176 is an eigenvector of Ag, '61 is an eigenvector of A1 and IE is an eigenvector of A2. (For each of the question parts, briey justify your answer and show your work stepbystep. Correct answers not supported by substantive explanations will receive no credit.) (a) (1 point) Without doing any calculations, nd a non-zero vector in Nul(A). (b) (1 point) Explain why {175, 171217;} is a linearly independent set. (c) (1 point) Are if and 17; in Col(A)? (d) (1 point) Find a basis for Col(A), if possible. (e) (1 point) Explain why the system A? = 175 has no solutions. (1') (1 point) Find the sum of the entries on the main diagonal of A. (g) (1 point) Find the determinant of A

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