LA2.1.16

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Solve for x given {\begin{vmatrix}x-2&2x-3&3x-4\\x-4&2x-9&3x-16\\x-8&2x-27&3x-64\end{vmatrix}}=0\,

By R_{1}-R_{2},R_{2}-R_{3}\,

{\begin{vmatrix}x-2&2x-3&3x-4\\x-4&2x-9&3x-16\\x-8&2x-27&3x-64\end{vmatrix}}={\begin{vmatrix}2&6&12\\4&18&48\\x-8&2x-27&3x-64\end{vmatrix}}\,

By applying C_{2}-2C_{1},C_{3}-3C_{1}\,

{\begin{vmatrix}2&2&6\\4&10&36\\x-8&-11&-40\end{vmatrix}}\,

2(2){\begin{vmatrix}1&1&3\\2&5&18\\x-8&-11&-40\end{vmatrix}}\,

By R_{2}-2R_{1},R_{3}+4R_{2}\,

4{\begin{vmatrix}1&1&3\\0&3&12\\x&9&32\end{vmatrix}}\,

Therefore 4[1(96-108)+x(12-9)]=0,3x-12=0,x=4\,


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