1. Find the inverse of matrix (if it exists). Do not use formula. 6271 2. The Inverse of matrix A is given. [3 2 11 1 1 2 1 2 Use the inverse to solve for X. A-1 = 3. If A and B are nxn matrices and A is Invertible. Prove: (ABA-)=ABA-. 4. Find a LU-factorization of the matrix and write our all elementary matrices and inverse of these elementary matrix. x + 3xy 2x -10x +2x3 = L AX = [1 0 5. Solve the linear system using LU-factorization. x-3x Coefficient matrix A-LU, where 0 01 1 0 -4 1. 12 1