Question
Find the values of the determinants : $\left|\begin{array}{cc}2 i & 3 \\ 4 & -i\end{array}\right|$
✓
Answer
$\begin{aligned}
& \left|\begin{array}{cc}
2 i & 3 \\
4 & -i
\end{array}\right| \\
= & 2 i(-i)-3(4) \\
= & -2 i^2-12 \\
= & -2(-1)-12 \ldots\left[\because i^2=-1\right] \\
= & 2-12 \\
= & -10
\end{aligned}
$
& \left|\begin{array}{cc}
2 i & 3 \\
4 & -i
\end{array}\right| \\
= & 2 i(-i)-3(4) \\
= & -2 i^2-12 \\
= & -2(-1)-12 \ldots\left[\because i^2=-1\right] \\
= & 2-12 \\
= & -10
\end{aligned}
$
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