Please use Python and Torch, don't use numpy.

4. Given a matrix A of size n xn where A= (4.1 Au A12 (A21 A22 A.2) Write a program that (a) Generates 4 matrices A11, A12, A21, A22 where A11 = A1:k, 1:k A22 = Ax+1:n,k+1:n where k is an input variable kn (b) Computes the product of the Schur complement with a vector, that is computes Sx = A223 A21A12 A1220 4. Given a matrix A of size n xn where A= (4.1 Au A12 (A21 A22 A.2) Write a program that (a) Generates 4 matrices A11, A12, A21, A22 where A11 = A1:k, 1:k A22 = Ax+1:n,k+1:n where k is an input variable kn (b) Computes the product of the Schur complement with a vector, that is computes Sx = A223 A21A12 A1220