Explore modern linear algebra concepts through hands-on Python programming in this comprehensive 2.5-hour tutorial. Dive into essential topics such as matrix operations, LU decomposition, inverse matrices, and null space calculations using the SymPy library. Master the Ordinary Least Squares method, implement the Gram-Schmidt process for QR decomposition, and understand the basics of Jacobian matrices and their application in neural networks. Gain practical skills by solving real-world problems and implementing algorithms, making linear algebra more accessible and applicable to data science and machine learning projects.