# Lineares Gleichungssystem/Mit Parameter/Lösungsgröße/Aufgabe/en

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We consider the linear system

${\displaystyle {\begin{matrix}2x&-ay&&=&-2\\ax&&+3z&=&3\\-{\frac {1}{3}}x&+y&+z&=&2\end{matrix}}}$

over the real numbers, depending on the parameter ${\displaystyle {}a\in \mathbb {R} }$. For which ${\displaystyle {}a}$ does the system of equations have no solution, one solution or infinitely many solutions?