Direct Methods for Solving Linear Equations

This lecture covers direct methods for solving systems of linear equations, focusing on LU factorization, forward and backward substitution, Gass elimination using pivoting, and the computational complexity of these methods. It also discusses the factorization of non-singular matrices into lower and upper triangular matrices, as well as sparse matrices and band matrices. Practical aspects such as visualizing non-zero elements, counting non-zero elements, and estimating computation time using MATLAB are explored.