This lecture covers modern numerical linear algebra focusing on matrix and vector operations, LU decomposition, Cholesky decomposition, QR decomposition, and Eigendecomposition. The goal is to utilize matrix properties for problem-solving. The instructor explains the algorithms for LU decomposition, forward/backward substitution, and the computational complexity involved. Additionally, the lecture introduces the Lotka-Volterra equations for predator-prey interactions and their simulation. The session concludes with a discussion on Prey-Predator Cycles and real data analysis.