Utlizing a Matlab routine:

4.15 (a) Write a routine that uses a one-sided plane rotation to syn lnetrize an arbitrary 2 2 matrix. That is, given a 2x2 matrix A, choose c and s so that c s1 12 11 012 =1b12 b22 is symmetric. (b) Write a routine that uses a two-sided plane rotation to annihilate the off-diagonal entries of an arbitrary 2 2 symmetric matrix. That is, given a symmetric 2 2 matrix B, choose e and s so that =10 d22 is diagonal. (c) Combine the two routines developed in parts a and b to obtain a routine for computing the singular value decomposition A-U?? of an arbitrary 2 x 2 matrix A. Note that U wil be a product to two plane rotations, whereas V will be a single plane rotation. Test your routine on a few randomly chosen 2 x 2 matrices and for a library SVD routine i compare the results with those By systematically solving successive 2 x 2 sub- problems, the module you have just developed can be used to compute the SVD of an arbi- trary m n matrix in a manner analogous to the Jacobi method for the symmetric eigen- value problem. 4.15 (a) Write a routine that uses a one-sided plane rotation to syn lnetrize an arbitrary 2 2 matrix. That is, given a 2x2 matrix A, choose c and s so that c s1 12 11 012 =1b12 b22 is symmetric. (b) Write a routine that uses a two-sided plane rotation to annihilate the off-diagonal entries of an arbitrary 2 2 symmetric matrix. That is, given a symmetric 2 2 matrix B, choose e and s so that =10 d22 is diagonal. (c) Combine the two routines developed in parts a and b to obtain a routine for computing the singular value decomposition A-U?? of an arbitrary 2 x 2 matrix A. Note that U wil be a product to two plane rotations, whereas V will be a single plane rotation. Test your routine on a few randomly chosen 2 x 2 matrices and for a library SVD routine i compare the results with those By systematically solving successive 2 x 2 sub- problems, the module you have just developed can be used to compute the SVD of an arbi- trary m n matrix in a manner analogous to the Jacobi method for the symmetric eigen- value