If \( \left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2...

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If \( \left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right| \neq 0 \), then the number of solutions of the system of equations \( a_{1} x+b_{1} y+c_{1} z=0, a_{2} x \) \( +b_{2} y+c_{2} z=0 \) and \( a_{3} x+b_{3} y+c_{3} z=0 \) is
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