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## Homework Statement

## Homework Equations

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.

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!