1. The problem statement, all variables and given/known data 2. Relevant equations A=LU, U^-1 * L^-1= A^-1 , U^-1 * L^-1 * U^-1 * L^-1 = A^-2, 3. The attempt at a solution I used MATLAB and the relations: U^-1 * L^-1= A^-1 , U^-1 * L^-1 * U^-1 * L^-1 = A^-2, to find a solution I found U^-1*L^-1 , let =B Then, found B^2 and took the inverse of B to get A^-2. B=A^-1 C=inv(B^2) so we have B*x+C*y= [2;5;10] My question is: is there an easier way to do this? We are supposed to do this problem by hand. This would have taken a good amount fo effort to find so many inverse matrices. Any input is appreciated! Thank you!