20. Cramer's Rule, Inverse Matrix, and Volume
OK, this is lecture twenty. And this is the final lecture on determinants. And it's about the applications. So we worked hard in the last two lectures to get a formula for the determinant and the properties of the determinant. Now to use the determinant and, and always this determinant packs all this information into a single number. And that number can give us formulas for all sorts of, things that we've been calculating already without formulas. Now what was A inverse? So, so I'm beginning with the formula for A inverse. Two, two by two formula we know, right? The two by two formula for A inverse, the inverse of a b c d inverse is one over the determinant times d a -b -c. Somehow I want to see what's going on for three by three and n by n. And actually maybe you can see what's going on from this two by two case. So there's a formula for the inverse, and what did I divide by? The determinant. So what I'm looking for is a formula where it has o...