Let
2 2 -4 10
A = 1 1 5 b = -2
1 3 6 -5
( A is 3 x 3 matrix and b is a vector)
1). Use Gaussian elimination with partial pivoting to find matrices L and U such that U is upper triangular, L is lower triangular with | l_ij| =< 1 for all i > j and LU = A', where A' can be obtained from A by interchanging rows.
2). Use LU decomposition to solve Ax = b