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Lecture 6: Column space and nullspace | Linear Algebra | Mathematics | MIT OpenCourseWare

This lecture discusses column space and nullspace. The column space of a matrix A tells us when the equation Ax = b will have a solution x. The nullspace of A tells us which values of x solve the equation Ax = 0. These video lectures of Professor Gilbert S

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Lecture 5: Transposes, permutations, spaces R^n | Linear Algebra | Mathematics | MIT OpenCourseWare

To account for row exchanges in Gaussian elimination, we include a permutation matrix P in the factorization PA = LU. Then we learn about vector spaces and subspaces; these are central to linear algebra. These video lectures of Professor Gilbert Strang tea

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Lecture 4: Factorization into A = LU | Linear Algebra | Mathematics | MIT OpenCourseWare

This session explains inverses, transposes and permutation matrices. We also learn how elimination leads to a useful factorization A = LU and how hard a computer will work to invert a very large matrix. These video lectures of Professor Gilbert Strang teac

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Lecture 3: Multiplication and inverse matrices | Linear Algebra | Mathematics | MIT OpenCourseWare

This lecture looks at matrix multiplication from five different points of view. We then learn how to find the inverse of a matrix using elimination, and why the Gauss-Jordan method works. These video lectures of Professor Gilbert Strang teaching 18.06 were

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Lecture 2: Elimination with matrices | Linear Algebra | Mathematics | MIT OpenCourseWare

This session introduces the method of elimination, an essential tool for working with matrices. The method follows a simple algorithm. To help make sense of material presented later, we describe this algorithm in terms of matrix multiplication. These video

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Lecture 1: The geometry of linear equations | Linear Algebra | Mathematics | MIT OpenCourseWare

A major application of linear algebra is to solving systems of linear equations. This lecture presents three ways of thinking about these systems. The “row method” focuses on the individual equations, the “column method” focuses on combining the co

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