First slide

Introduction to Determinants

Question

$| \begin{matrix} \sin^{2} x & \cos^{2} x & 1 \\ \cos^{2} x & \sin^{2} x & 1 \\ - 10 & 12 & 2 \end{matrix} | =$

Easy

A

0
B

$12 \cos^{2} x - 10 \sin^{2} x$
C

$12 \sin^{2} x - 10 \cos^{2} x - 2$
D

$10 \sin 2 x$

Solution

Applying $C_{1} \to C_{1} + C_{2},$ we get $| \begin{matrix} 1 & \cos^{2} x & 1 \\ 1 & \sin^{2} x & 1 \\ 2 & 12 & 2 \end{matrix} | = 0$

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