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I assume your students have seen Linear Algebra. Remember in Linear Algebra how you sometimes have to solve $Ax = b$ for a matrix $A$ with more columns than rows? You usually get free variables, right? So after reducing to echelon form you have something like: $$\begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & -1 \end{pmatrix}\begin{pmatrix} x \\ y \\ z \...


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