Channel: MyWhyU

Category: Education

Tags: row reductionmathematicssimultaneous equationsalgebramatrixdependent systemaugmented matrixinfinite solution setinfinitely many solutionsgauss-jordan eliminationwhyuprofessor von schmohawkmatriceswhy usubspacelinear equationfree variablesystem of linear equationsreduced row echelon formpivot columnmathsystem of equationsparametric equationspivot positiondimensions

Description: This chapter introduces the concept of “pivot columns” and shows how they can be used to determine whether a system of linear equations has a single unique solution, no solutions, or infinitely many solutions, simply by looking at the positions of the pivot columns within the reduced row echelon form matrix. If the system has infinitely many solutions, we then see how a set of parametric equations can be easily produced from that matrix. This chapter also examines how the solution set of a system of linear equations forms a subspace of lower dimensionality than the system itself.