Why Solve for the Pivots in Reduced Row Echelon Form

[DividedByZero]

Hello Everybody,

 

I'm curious to know why we solve for the pivot variables when we reduce a matrix to reduced row echelon form and are trying to find a solution.

 

Thank you

[imatfaal]

Gilbert Strang's course on linear algebra is all one line here Whilst the members can answer your question; I would doubt you could get a better teacher