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

English

Gujarati

Hindi

3 and 4 .Determinants and Matrices

normal

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

Share

Similar Questions

If ${a_1},{a_2},{a_3}…..{a_n}….$ are in $G.P.$ then the value of the determinant $\left| {\,\begin{array}{*{20}{c}}{\log {a_n}}&{\log {a_{n + 1}}}&{\log {a_{n + 2}}}\\{\log {a_{n + 3}}}&{\log {a_{n + 4}}}&{\log {a_{n + 5}}}\\{\log {a_{n + 6}}}&{\log {a_{n + 7}}}&{\log {a_{n + 8}}}\end{array}\,} \right|$ is

medium

(AIEEE-2005)

If $x + y – z = 0,\,3x – \alpha y – 3z = 0,\,\,x – 3y + z = 0$ has non zero solution, then $\alpha = $

medium

Let $ \alpha _1, \alpha _2$ are two values of $\alpha $ for which the system $2 \alpha x + y = 5, x – 6y = \alpha $ and $x + y = 2$ is consistent, then $ |2(\alpha _1 + \alpha _2)| $ is –

normal

The system of equations $x + y + z = 6$, $x + 2y + 3z = 10,x + 2y + \lambda z = \mu $, has no solution for

hard

The cubic $\left| {\begin{array}{*{20}{c}}
0&{a – x}&{b – x} \\
{ – a – x}&0&{c – x} \\
{ – b – x}&{ – c – x}&0
\end{array}} \right| = 0$ has a reperated root in $x$ then,

normal