Question

The value of the determinant $\left| \begin{matrix} 31 & 37 & 92 \\ 31 & 58 & 71 \\ 31 & 105 & 24 \end{matrix} \right|$is.

• A. – 2
• B. 0
• C. 81
• D. None of these

Answer 1

Answer: (B)

0

Answer 2

$\left| \begin{matrix} 31 & 37 & 92 \\ 31 & 58 & 71 \\ 31 & 105 & 24 \end{matrix} \right| = \left| \begin{matrix} 31 & 37 & 92 \\ 0 & 21 & - 21 \\ 0 & 47 & - 47 \end{matrix} \right|$;by $R_{3} \rightarrow R_{3} - R_{2}$ $$R_{2} \rightarrow R_{2} - R_{1}$$

= $\left| \begin{matrix} 31 & 129 & 92 \\ 0 & 0 & - 21 \\ 0 & 0 & - 47 \end{matrix} \right|$ = 0; (by $C_{2} \rightarrow C_{2} + C_{3})$.