Chapter 1 · Linear Algebra (MIT)

Unit I: Ax = b and the Four Subspaces

The geometry of linear equations, elimination, matrix multiplication and inverses, A = LU, transposes and permutations, vector spaces, column space and nullspace, solving Ax = 0 and Ax = b, independence, basis and dimension, the four fundamental subspaces, and graphs and networks, with the unit's review and exam.