Elimination and Factorization A = CR

This 37-minute lecture from the "A Vision of Linear Algebra" series explores elimination and the column-row factorization A = CR. Taught by Professor Gilbert Strang at MIT, learn how a matrix A with rank r has a row echelon form containing the identity matrix in its first r independent columns. Discover the significance of matrix F in the remaining n−r columns of the echelon form, which multiplies the first r independent columns to produce the dependent columns. Understand how F reveals bases for both the row space and nullspace of the original matrix A, and how it enables the important column-row factorization A = CR. Part of MIT OpenCourseWare's freely available educational content under a Creative Commons BY-NC-SA license.