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

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The determinant \( \left|\begin{array}{lll}b_{1}+c_{1} & c_{1}+a_{1} & a_{1}+b_{1} \\ b_{2}+c_{2} & c_{2}+a_{2} & a_{2}+b_{2} \\ b_{3}+c_{3} & c_{3}+a_{3} & a_{3}+b_{3}\end{array}\right|= \)
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(1) \( \left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right| \)
(2) \( 2\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right| \)
(3) \( 3\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right| \)
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