Algebra 60 - Parametric Equations with Gauss-Jordan Elimination

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.

[Golden_Tortoise]

Thank you so much for the videos! I now understand math better than all of my years in high school and college.

[revolutionnaman]

Chapter Algebra 60-Parametric Equations with Gauss-Jordan Elimination @14:26, the graph of the solution set should be parallel to y-axis as well as to z-axis because in the equivalent reduced row-echelon form y and z are the free variables and only x is the dependent variable, but Mr. Professor Von-Schmohawk says otherwise.
Please resolve my query. hoping for a quick reply. 
Thank You for making such brilliant series on Algebra, otherwise we wouldn't have never visualised algebra in the real world.

[diamondwhite]

im just watching this to remind myself that math gets infinitely more complicated

[abdulqadirafridi]

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[MegaMementoMori]

If you multiply (y-[1/4]z=[3/2]) by 2, which gives (2y-[1/2]z=3) and then subtract it from (x-[1/2]z=-1), you would get (x-2y=4).In what way would this equation be significant?