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... 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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