Useing R code to solve below questions

The problem For the relevant matrix X corresponding to your last digit of your student ID: 1. Compute the singular value decomposition of X = UDVT. Report D. 2. Using the results you just obtained with eigenvalues di, d2, ... in decreasing order and corresponding eigenvectors ui, u2, ... and V1, V2, ..., compute and report a series of approximations to X using sums of rank one matrices. The approximations are djujv1, diujv1 +d2u2v, ... Comment on your results. 3. Perform and report the Karhunen-Loeve decomposition of XlX. 4. Based upon your numerical results, briefly discuss what is the link between the singular value decomposition of X and the Karhunen-Loeve decomposition of xTx. ID ending in 8 x] x2x3 _4 -4 -U -4 _6 _4 2-80 -4 ? 80 446. 8 20 890. The problem For the relevant matrix X corresponding to your last digit of your student ID: 1. Compute the singular value decomposition of X = UDVT. Report D. 2. Using the results you just obtained with eigenvalues di, d2, ... in decreasing order and corresponding eigenvectors ui, u2, ... and V1, V2, ..., compute and report a series of approximations to X using sums of rank one matrices. The approximations are djujv1, diujv1 +d2u2v, ... Comment on your results. 3. Perform and report the Karhunen-Loeve decomposition of XlX. 4. Based upon your numerical results, briefly discuss what is the link between the singular value decomposition of X and the Karhunen-Loeve decomposition of xTx. ID ending in 8 x] x2x3 _4 -4 -U -4 _6 _4 2-80 -4 ? 80 446. 8 20 890