We introduced the LU-decomposition as a method for solving a linear system of equations. However, until now we have only decomposed the matrix A into L and U. Obviously, we now want to take the second step and see that this matrix decomposition helps us in solving a linear system of equations.
For this we return to the system of Eq. 25.2 from which we also took the matrix. The right-hand side is
Calculating . We first solve Eq. ...