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Question Number 15193 by arnabpapu550@gmail.com last updated on 08/Jun/17

The value of the determinant  △= determinant (((   2a_1 b_1 ),(a_1 b_2 +a_2 b_1 ),(a_1 b_3 +a_3 b_1 )),((a_1 b_2 +a_2 b_1 ),(    2a_2 b_2 ),(a_2 b_3 +a_3 b_2 )),((a_1 b_3 +a_3 b_1 ),(a_3 b_2 +a_2 b_3 ),(    2a_3 b_3 )))is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{determinant} \\ $$$$\bigtriangleup=\begin{vmatrix}{\:\:\:\mathrm{2}{a}_{\mathrm{1}} {b}_{\mathrm{1}} }&{{a}_{\mathrm{1}} {b}_{\mathrm{2}} +{a}_{\mathrm{2}} {b}_{\mathrm{1}} }&{{a}_{\mathrm{1}} {b}_{\mathrm{3}} +{a}_{\mathrm{3}} {b}_{\mathrm{1}} }\\{{a}_{\mathrm{1}} {b}_{\mathrm{2}} +{a}_{\mathrm{2}} {b}_{\mathrm{1}} }&{\:\:\:\:\mathrm{2}{a}_{\mathrm{2}} {b}_{\mathrm{2}} }&{{a}_{\mathrm{2}} {b}_{\mathrm{3}} +{a}_{\mathrm{3}} {b}_{\mathrm{2}} }\\{{a}_{\mathrm{1}} {b}_{\mathrm{3}} +{a}_{\mathrm{3}} {b}_{\mathrm{1}} }&{{a}_{\mathrm{3}} {b}_{\mathrm{2}} +{a}_{\mathrm{2}} {b}_{\mathrm{3}} }&{\:\:\:\:\mathrm{2}{a}_{\mathrm{3}} {b}_{\mathrm{3}} }\end{vmatrix}\mathrm{is} \\ $$

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