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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:
$\begin{vmatrix}2&3&7\\13&17&5\\15&20&12 \end{vmatrix}$
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Answer

$\begin{vmatrix}2&3&7\\13&17&5\\15&20&12 \end{vmatrix}$
Use: $R_3 \rightarrow R_3 - R_2$
$=\begin{vmatrix}2&3&7\\13&17&5\\2&3&7 \end{vmatrix}$
$=0$
$\because\text{R}_3=\text{R}_1$

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