If we have a matrix
We can't write -- a result would require division.
So... Can we find ?
We sure can! It's called an inverse matrix. Here's how you find it:
Let's start with this matrix
This is going to work a lot like Gaussian elimination. (If you've ever seen that before.)
We make a big double matrix
A on this side... the identity on this side.
The goal is to use row operations (like you did with Gaussian elimination) to...