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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
Evaluate the determinant $\Delta=\left|\begin{array}{rrr}1 & 2 & 4 \\ -1 & 3 & 0 \\ 4 & 1 & 0\end{array}\right|$
  • A
    $-50$
  • B
    $-51$
  • ✓
    $-52$
  • D
    $-53$
✓

Answer

Correct option: C.
$-52$
c
Note that in the third column, two entries are zero. So expanding along third column  $\left(\mathrm{C}_{3}\right),$ we get

$\begin{aligned}
\Delta &=4\left|\begin{array}{cc}
-1 & 3 \\
4 & 1
\end{array}\right|-0\left|\begin{array}{cc}
1 & 2 \\
4 & 1
\end{array}\right|+0\left|\begin{array}{cc}
1 & 2 \\
-1 & 3
\end{array}\right| \\
&=4(-1-12)-0+0=-52
\end{aligned}$

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