Channel: MyWhyU

Category: Education

Tags: why urow reductionelementary row operationindependent equationmathematicsindependent systemlinear equationsimultaneous equationslinear combinationalgebrasystem of linear equationsreduced row echelon formmatrixdependent systemaugmented matrixdependent equationgauss-jordan eliminationwhyuprofessor von schmohawkmathmatricessystem of equations

Description: This chapter builds on Algebra chapter 57 which explained the concept of dependency. In this chapter, we see that although it can sometimes be difficult to spot when a system of linear equations is dependent, when a dependent system is represented in matrix form and simplified through Gauss-Jordan elimination, an equivalent independent system is automatically produced. This equivalent system typically contains fewer equations, with fewer variables in each equation. From this simpler system, a parametric representation of the solution set can then be easily written.