A=LU, U^-1 * L^-1= A^-1 , U^-1 * L^-1 * U^-1 * L^-1 = A^-2,
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.
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!