Solve Using LU Decomposition

This example shows how to use LU Decomposition to solve a linear system of equations.

Problem:

Suppose we have:

Solve for for

Solution:

First we define and write our initial system as: . We start by solving the our modified system:

Inspecting the first line we realize this is easy to solve using Forward Substitution, solving for gives us:
Next we solve the equation defined at the beginning:

Inspecting the last line we realize this is easy to solve using Backward Substitution, solving for gives us: