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Determinants — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDeterminants5 Marks
Question
Without expanding, show that the values of the following determinant are zero: $\begin{vmatrix}6&-3&2\\2&-1&2\\-10&5&2 \end{vmatrix}$
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Answer

$\triangle=\begin{vmatrix}6&-3&2\\2&-1&2\\-10&5&2 \end{vmatrix}$
$\Rightarrow\triangle=\begin{vmatrix}0&-3&2\\0&-1&2\\0&5&2 \end{vmatrix} [$Applying $C_1 \rightarrow C_1 + 2C_2]$
$\Rightarrow\triangle=0$

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