(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Matrix problems

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