Lecture 9
Linear transformations continued: invertible and singular. Characteristic root (eigenvalue). For matrices: a law for multiplying a column vector by a matrix.
Lecture 10
Matrix Algebra and solving linear systems, forming the augmented matrix. Solving with elementary row operations (defined). Properties of row operations (invertibility etc).
Lecture 11 and 12
Solving systems of linear equations. Definition of row echelon form and reduced row echelon form. Examples of Gaussian elimination and Gauss-Jordan elimation. Comment on homogeneous linear equations. Definition of rank.