Hi Sean,
Perhaps you could tell us the exact problem for which you are trying to program a solution. Otherwise (as you can see) all you will get is people relating to their own experience with linear algebra in school. Linear algebra is a very large field. You can solve for the electron density in an unstable molecule, the engine firing times in a flight to the moon, or how much a teenager with too many life complications makes at his part time job. The steps to do any of that are different.
So yeah, folks here CAN help you, but you need to come clean and precisely describe your problem.
I suspect however that you are only looking for an answer to an extra credit problem, and won't be back.
Hopefully I am wrong.