Description

If a matrix A has rank r, then its row echelon form (after elimination) contains the identity matrix in its first r independent columns. How do we interpret the matrix F that appears in the remaining n − r columns of that echelon form? F multiplies those first r independent columns of A to give its n − r dependent columns. Then F reveals bases for the row space and the nullspace of the original matrix A. And F is the key to the column-row factorization A = CR.

Slides Used in this Video: Elimination and Factorization A = CR (PDF)

Instructor: Gilbert Strang