4. (20 points) Let 7: R3 -> R3 be given by projection onto the plane P := {(x,y, z) ER | x + 2y + 32 = 0}. In formulas, this means that if v E R3 and v = s +t for s E P and te PL, then T(v) = s. (a) (5 points) Choose two different bases 3 and y for 3. i. compute [T]s and [Tly. ii. write down the change of coordinate matrix Q such that [T]s = Q-' [T], Q. 1 (b) (6 points) Compute the characteristic polynomial of T and find the eigenvalues of T. Find the algebraic multiplicity of each eigenvalue. (c) (7 points) Compute the eigenspaces of T and compute the geometric multiplicities of each eigenvalue. (d) (2 points) Is T diagonalizable? Why or why not