Instructor: Gilbert Strang The Help Session Videos were developed by: Martina Balagovic, Linan Chen, Benjamin Harris, Ana Rita Pires, David Shirokoff, Nikola... This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. I have been tutoring math 51 for over three years and using linear algebra in advanced mathematics and computer science course work and as an software engineer. I know this material like the back of my hand, and I’ve worked with such a huge number of diverse students that I feel like know where students get confused, and how students succeed. This is the fourth post in an article series about MIT's Linear Algebra course. In this post I will review lecture four on factorizing a matrix A into a product of a lower-triangular matrix L and an upper-triangular matrix U, or in other words A=LU. The lecture also shows how to find the inverse of matrix product A·B, how to find the inverse of transposed matrix A T, and introduces permutation matrices. 18.06 Linear Algebra - The video lectures are on web.mit.edu/18.06 and ocw.mit.edu and YouTube. Many universities use the textbook Introduction to Linear Algebra. 18.085 / 18.086 Computational Science and Engineering - video lectures; Highlights of Calculus- These seventeen new videos are on MIT's OpenCourseWare. Course Description This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices. Compared with Linear Algebra (18.06), more emphasis is placed on theory and proofs.