So I'm still learning about pivots in matrices. I've got this question that says
Suppose that the augmented matrix associated to a system of linear equations has a pivot in every column.
I had 4 answers to choose from on which was true and I believe that this means that since there is a pivot in every column then there is a unique solution to the system. Am I write on this? I'm practicing for an upcoming exam more or less on these 'find the true statement' types.
No - there could be a pivot in the augmented column. Consider: $$ \left[\begin{array}{cc|c} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 0 & 0 & 1 \\ \end{array}\right] $$