Lecture 21
Determinants: definition and properties (presented as theorems). The effects of ero's on determinants.
Lecture 22
Det(A) = Det(A transpose). Cramer's rule. The determinant and criteria for invertibility
Lecture 23 and 24
Eigenvalues and eigenvectors. Definitions and examples. The characteristic equation. Determinant and trace in terms of eigenvalues. Linear independence of the eigenvectors corresponding to difference eigenvalues of a matrix. Decompostion (diagonalisation) of A in terms of matrices of eigenvalues and eigenvectors. Using this to calculate A raised to a power.