Comment by mannykannot

I think you are doing a great job here. I looked through your sections on determinants and inverses, and it is so much better than the way I was taught: "this is the formula for inverting a 2x2 matrix. This bit is called the determinant." For me, learning always works best when I know what we are working towards and seeing how it works, and putting the formal definition first is rarely effective in that. Start with a specific example, concrete where possible, and generalize from that.