If x, y, z are not all simultaneously equal to zero, satisfying system of equations ( sin 3 θ ) x -

English

Gujarati

Hindi

3 and 4 .Determinants and Matrices

normal

If $x, y, z$ are not all simultaneously equal to zero, satisfying the system of equations

($\sin 3 \theta ) x - y + z = 0$
($\cos 2 \theta ) x + 4 y + 3 z = 0$
$2 x + 7 y + 7 z = 0$
then the number of principal values of $\theta$ is

A

$2$

B

$4$

C

$5$

D

$6$

Solution

$\theta = n \pi + (- 1)^n$ . $\frac{\pi }{6}$ or $n \pi$

Standard 12

Mathematics

Share

Similar Questions

If the system of linear equations $x_1 + 2x_2 + 3x_3 = 6$ ; $x_1 + 3x_2 + 5x_3 = 9$ ; $2x_1 + 5x_2 + ax_3 = b$ is consistent and has infinite number of solutions, then

hard

(JEE MAIN-2013)

Number of value of $'a'$ for which the system of equations,$A^2 x + (2 – a) y = 4 + a^2$ $a x + (2 a – 1) y = a^5 – 2$ possess no solution is

normal

Examine the consistency of the system of equations. $2 x-y=5$ ; $x+y=4$

medium

Solve system of linear equations, using matrix method. $2 x-y=-2$ ; $3 x+4 y=3$

medium

Solve system of linear equations, using matrix method. $x-y+2 z=7$ ; $3 x+4 y-5 z=-5$ ; $2 x-y+3 z=12$

hard