8. Consider the matrix A = (a) Verify that A = 2 is the only eigenvalue of matrix A. (b) Determine a basis for the eigenspace of the matrix A corresponding to the eigenvalue A = 2. Is A diagonalizable? Explain. (c) Solve the linear system (A -A/)x = v1, where v1 is an eigenvector of the matrix A with eigenvalue A = 2. Choose v2 to be a specific solution to this system. (d) Solve the linear system (A - A/)x = v2, where v2 is the solution to (A - A/)x = v1 that you solved for in the previous part. Choose va to be a specific solution to this system. (e) Let B = {v1, v2, va}, using the vectors from the previous problems. Verify that B is a basis for R. (f) Compute Av1, Av2, and Avg using coordinates relative to the basis B. You should do this first by using the relationships between v, and v2 and then check your answer by direct computation. (g) Finally, determine the matrix / which represents the transformation 7: R - R3, T(x) = Ax with coordinates relative to the basis B