Find the values of following determinants. (1) | cc -1 & 7 2 & 4 … - Vidyadip

Question

Find the values of following determinants.
(1) $\left|\begin{array}{cc}-1 & 7 \\ 2 & 4\end{array}\right|$
(2) $\left|\begin{array}{cc}5 & 3 \\ -7 & 0\end{array}\right|$
(3) $\left|\begin{array}{ll}\frac{7}{3} & \frac{5}{3} \\ \frac{3}{2} & \frac{1}{2}\end{array}\right|$

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Answer

we know, determinant of a $2 \times 2$ matrix
$\left|\begin{array}{ll}
a & b \\
c & d
\end{array}\right|$
(1) $(-1 \times 4)-(7 \times 2)=-4-14=-18$
(2) $(5 \times 0)-(3 \times-7)=0-(-21)=21$
$\begin{aligned}
& \text { (3) } \frac{7}{3} \times \frac{1}{2}-\frac{5}{3} \times \frac{3}{2}=\frac{7}{6}-\frac{15}{6} \\
& =-\frac{8}{6} \\
& =-\frac{4}{3}
\end{aligned}$

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