Answer
See explanation
Work Step by Step
If matrix has pivot position in every column, then columns must be linearly independent.
Because columns are linearly independent, system must have unique solution.
Coefficient matrix with 3 pivot columns:
$\left[\begin{array}{lll}* & - & - \\ 0 & * & - \\ 0 & 0 & *\end{array}\right]-\left[\begin{array}{l}- \\ - \\ -\end{array}\right]$
where asterix represents any nonzero number and - represents any number
It is easy to see that solution is unique using back substitution to solve.
