Matrix Determinants: Operations and Theorems

This lecture covers the calculation of determinants using operations on matrices, such as adding a multiple of one row to another, swapping rows, and multiplying a row by a constant. The instructor demonstrates the application of these operations to find the determinant of a matrix. The lecture also presents the theorems related to determinants, including the theorem for triangular matrices and the theorem for determining the invertibility of a matrix based on its determinant. The instructor explains the importance of these theorems in understanding the properties of matrices and their determinants.