Algebra 56 - A Geometrical View of Gauss-Jordan Elimination -

Although Gauss-Jordan Elimination is typically thought of as a purely algebraic process, when viewed geometrically, this process is beautiful and amazing, providing insights into the underlying mechanisms of the matrix transformations which lead to the solutions of a system of linear equations. Since a system of linear equations in three variables is graphically represented by a collection of planes, following how these planes change their orientation with each row operation can give us an intuitive understanding of how the transformation to reduced row echelon form works.