P3 [Discovery proof of SVD for a 2 2 matrix] Let A a) Verify that the vectors vi [cos 0 sin 0 and v2 = [-] sin 0 cos 0 are orthonormal for any choice of the parameter 0 0. f) Assume tan 20 = with cos 20 0 and let u Av2. Explain why = = Avi, uz U = = [u | u], = | 0 002] and V = [p| v2] provide a SVD decomposition A = UV of A. g) (MATLAB) Numerically compare the decomposition obtained in f) with the results of the MATLAB function svd for the two angles 0 satisfying tan 20 = with cos 20 0.