Please help me on all parts of question 8. It is due tomorrow. Thank you very much!
8. * This problem will help yow work through computing the SVD in the more general case, when one or more of the singular values (or just the eigenvalues of AT A) is repeated. Let 13) -6 18 8 24 12 (a) Compute the eigenvalues and eigenvectors of ATA. Note that there are two eigen- vectors with the same eigenvalue Q.
(b) Note that the second two vectors are orthogonal to the first vector, but not to each other. Therefore we must divide the first vector by it's length, but do Gram Schmidt on the remaining two vectors to get an orthonormal basis (not just any basis) to give the columns of V. Using Gram Schmidt, find V (c) Compute the corresponding left singular vectors of A. The first left singular vector can be computed at usual, but since the second singular value is 0, we can either solve for the left singular vector by finding another eigenvalue of AAT or by finding a basis for the space perpendicular to the first left singular vector. (d) Finally give an SVD for A