Lecture 13
Definitions of transpose (and some properties) and trace. Definition of row equivalence and elementary matrices.
Lecture 14
Recap of Gauss-Jordan strategy to solve a system of linear equations. Discussion and examples of the link between solutions and linear independence of rows and colums of the matrix, A.
Lecture 15 and 16
Theorem on equivalent statements to "A is invertible". Special matrices and their inverses: diagonal, triangular (upper and lower). Proofs of some properties of these matrices eg. on the invertibility of diagonal and triangular matrices, products and inverses of upper and lower triangular matrices.