Prove that \( \Delta=\left|\begin{array}{ccc}\beta \gamma & \beta \gamma^{\prime}+\beta^{\prime}...
Prove that \( \Delta=\left|\begin{array}{ccc}\beta \gamma & \beta \gamma^{\prime}+\beta^{\prime} \gamma & \beta^{\prime} \gamma^{\prime} \\ \gamma \alpha & \gamma \alpha^{\prime}+\gamma^{\prime} \alpha & \gamma^{\prime} \alpha^{\prime} \\ \alpha \beta & \alpha \beta^{\prime}+\alpha^{\prime} \beta & \alpha^{\prime} \beta^{\prime}\end{array}\right|=\left(\alpha \beta^{\prime}-\alpha^{\prime} \beta\right)\left(\beta \gamma^{\prime}-\beta^{\prime} \gamma\right)\left(\gamma \alpha^{\prime}-\gamma^{\prime} \alpha\right) \)
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