Value of $left| {begin{array}{*{20}{c}} 1&x&y 2&{sin x + 2x}&{sin y + 2y} 3&amp

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3 and 4 .Determinants and Matrices

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The value of $\left| {\begin{array}{*{20}{c}}
1&x&y\\
2&{\sin x + 2x}&{\sin y + 2y}\\
3&{\cos x + 3x}&{\cos y + 3y}
\end{array}} \right|$ is

A

$cos(x + y)$

B

$cos(xy)$

C

$sin(x + y)$

D

$sin(x - y)$

Solution

$\mathrm{R}_{2} \rightarrow \mathrm{R}_{2}-2 \mathrm{R}_{1} $ and $ \mathrm{R}_{3} \rightarrow \mathrm{R}_{3}-3 \mathrm{R}_{1}$

$\left|\begin{array}{ccc}{1} & {x} & {y} \\ {0} & {\sin x} & {\sin y} \\ {0} & {\cos x} & {\cos y}\end{array}\right|=\sin (x-y)$

Standard 12

Mathematics

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