(24 points) Let A = (4 -) Find the eigenvalues and corresponding eigenspaces for A. and U2 one from each eigenspace of A and verify that (b) Choose two eigenvectors H = [U1, U2] is a basis for R?. (c) If x = (0,6)T, find [xJn and use these coordinates to write X as a linear combination of U1 and U2. Use this representation to calculate A*x; making use of the properties of U1 and U2. Write your final answer as a vector with standard coordinates (i.e. the eigenvalues of A with respect to the standard basis for R?).