Consider a linear system whose augmented matrix is of the form $$ \left[ \begin{array}{ccc|c} 1&2&1&1\\ -1&4&3&2\\ 2&-2&a&3 \end{array} \right] $$
For what values of a will the system have a unique solution?
$$ \left[ \begin{array}{ccc|c} 1&2&1&1\\ -1&4&3&2\\ 2&-2&a&3 \end{array} \right] \to \left[ \begin{array}{ccc|c} 1&2&1&1\\ 0&6&4&3\\ 0&-6&a-2&1 \end{array} \right] \to \left[ \begin{array}{ccc|c} 1&2&1&1\\ 0&6&4&3\\ 0&0&a+2&4 \end{array} \right] $$
The system has a unique solution because is consistent and a+2≠0 and a≠-2
I've done this part, but I'm not sure, if they could help me I'd appreciate it.