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)$\left|\begin{array}{cc}\frac{7}{3} & \frac{5}{3} \\ \frac{3}{2} & \frac{1}{2}\end{array}\right|$

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Answer

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

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