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Suppose that you are given the linear system:

$$ \begin{align} 2x + 3y + z & = 1 \\\ x – y – z & = 0 \\\ 0x + 2y + 2z & = 2 \end{align}$$

Determine if the system is consistent and, if so, find all solutions.

The system is inconsistent.

The system is consistent with unique solution $(1,-1,2)$.

The system is consistent with unique solution $(1,0,2)$.

The system is consistent with solution set $\{ (t,-t,t2): t \in \mathbb{R} \}$.

The system is consistent with solution set $\{(t,0,2t): t \in \mathbb{R} \}$.