1. The problem statement, all variables and given/known data 1)Find all matrices X that satisfy the equation A*X*B^T = C, in terms of the LU factorizations of A and B. State the precise conditions under which there are no solutions. B^T is the transpose of B. 2) Let U_1 and U_2 be two upper-triangular matrices. Let Z be an m × n matrix. Let X be an unknown matrix that satisfies the equation U_1X + XU_2 = Z. A. Give an algorithm to find X in O(mn(m+ n)) flops (floating-point operations). B. Find conditions on U_1 and U_2 which guarantee the existence of a unique solution X. C. Give a non-trivial example (U_1 is not equal to 0, U_2 is not equal to 0, X is not equal to 0) where those conditions are not satisfied and U_1X + XU_2 = 0. 2. Relevant equations 3. The attempt at a solution any hints?