Elimination and Factorization A = CR

A Vision of Linear Algebra
Instructor: Gilbert Strang
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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

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Post from MIT OpenCourseWare on March 12, 2025

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