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: