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 ...

I know to find if a set of vectors are linearly indepenent I have to put them in a matrix and get the rref. if the rref == the identity matrix, then the vectors are linearl independent.