Can I please have help with this question? Thanks

Problem 3 Find all matrices X that satisfy the equation AXB = C, in terms of the LU factorizations of A and B. State the precise conditions under which there are no solutions. Problem 4 Let Uj and U2 be two upper-triangular matrices. Let Z be an m x n matrix. Let X be an unknown matrix that satisfies the equation UlX + XU2 = Z. A. Give an algorithm to find X in O(mn(m + n)) flops (floating-point operations). B. Find conditions on Uj and U2 which guarantee the existence of a unique solution X. C. Give a non-trivial example (U1 7 0, U2 * 0, X * 0) where those conditions are not satisfied and U1X + XU2 = 0