Back Substitution: an example

We are given an upper triangular matrix from the decomposition and the vector from the (forward substitution)[forward_example.md] step:

that, in our 4x4 example, becomes:

Now we solve for the vector using back substitution.

System to solve:

Back Substitution Steps:

We will start from the last equation (the bottom row) and work our way upwards, solving for each one by one.

1. Solve for from the last equation:

2. Solve for from the third equation:

3. Solve for from the second equation:

4. Solve for from the first equation: