Matrix Factorization: LU Decomposition

This lecture covers the LU decomposition method for solving systems of linear equations. The instructor explains the process of factorizing a matrix into lower and upper triangular matrices, highlighting the importance of using elementary row operations. The lecture demonstrates how to calculate determinants of matrices, introducing the concept of cofactors and their role in simplifying determinant calculations. The instructor emphasizes the recursive nature of determinant calculations and provides insights into the significance of matrix invertibility. Practical examples and step-by-step explanations help students understand the LU decomposition method and its applications in solving large systems of equations.