Channel: MyWhyU

Category: Education

Tags: why uschmohawkrow reductionelementary row operationeducationalmathematicslinear equationsimultaneous equationsalgebrasystem of linear equationsreduced row echelon formmatrixaugmented matrixsolving systems of linear equationsgauss-jordan eliminationwhyuvon schmohawkprofessor von schmohawkmathmatricessystem of equations

Description: 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.