More Problems on Linear Systems and Matrices

Problem. Consider the linear system

\begin{displaymath}\left\{\begin{array}{lcl}
x + 3y - z &=& a \\
x + 2y &=& b \\
3x + 7y - z &=& c \\
\end{array} \right.\end{displaymath}

1.
Find the necessary and sufficient conditions on $a$, $b$, and $c$for the above system to be consistent.
2.
Discuss your answer (to (1)) when

\begin{displaymath}a=1,\; b=1,\; c=3\end{displaymath}

and

\begin{displaymath}a=1,\; b=0,\; c=-1\end{displaymath}

Answer.


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