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3 and 4 .Determinants and Matrices
easy
નિશ્ચાયક $\Delta=\left|\begin{array}{rrr}1 & 2 & 4 \\ -1 & 3 & 0 \\ 4 & 1 & 0\end{array}\right|$ નું મૂલ્ય મેળવો.
A
$-50$
B
$-51$
C
$-52$
D
$-53$
Solution
Note that in the third column, two entries are zero. So expanding along third column $\left(\mathrm{C}_{3}\right),$ we get
$\begin{aligned}
\Delta &=4\left|\begin{array}{cc}
-1 & 3 \\
4 & 1
\end{array}\right|-0\left|\begin{array}{cc}
1 & 2 \\
4 & 1
\end{array}\right|+0\left|\begin{array}{cc}
1 & 2 \\
-1 & 3
\end{array}\right| \\
&=4(-1-12)-0+0=-52
\end{aligned}$
Standard 12
Mathematics
