Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...
My understanding of linear independance is that if you have a unique solution after rref, it's linear independant. If you have multiple solutions or no solution, it's not linear ...
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