Suppose T : R4 →R4 with T(x) = Ax is a linear transformation such that • (0,0,1,0) and (0,0,0,1) lie in the kernel of T, and • all vectors of the form (x1,x2,0,0) are reflected about the line 2x1 −x2 = 0. (a) Compute all the eigenvalues of A and a basis of each eigenspace. (b) Is A invertible? Explain. (c) Is A diagonalizable? If yes, write down its diagonalization (you can leave it as a product of matrices). If no, why not?