(8) Suppose T : R 4 ? R 4 with T(x) = Ax is a lineartransformation such that • (0, 0, 1, 0) and (0, 0, 0, 1) lie in thekernel of T, and • all vectors of the form (x1, x2, 0, 0) arereflected about the line 2x1 ? x2 = 0.
(a) Compute all the eigenvalues of A and a basis of eacheigenspace.
(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?
