Episode 05c (36:06):
Secrets of the inverse
For our method of finding inverses, we gain power by replacing our row operations with elimination matrices. Inverses are a product of permutation matrices and elimination matrices. Soon we will need the inverse of elimination matrices themselves and we show these are very simple. We also find that if an inverse does not exist, one or more pivots are missing, and the same it true for linear dependence between columns (a big deal coming up). Cats love matrices.
Best dined upon by 2016/09/12
To be fixed: @7:47, the hand/brain/mouth system goes wrong and then -4 in the 2,1 position should be -2.