Home
Class 12
MATHS
Find the value theta for which the homog...

Find the value `theta` for which the homogeneous system of equations: `(sin 3 theta) x-y+z=0 , (cos2theta) x+4y+3z=0` and 2x+7y+7z=0 has non-trivial solutions.

Text Solution

Verified by Experts

The correct Answer is:
`|{:(sin3theta,-1,1),(cos2theta,4,3),(2,7,7):}|=0`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CHHAYA PUBLICATION|Exercise EXERCISE 2A|36 Videos

  • DETERMINANT

    CHHAYA PUBLICATION|Exercise EXERCISE 2B|111 Videos

  • DEFINITE INTEGRAL AS AN AREA

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

Find the value of lambda for which the homogeneous system of equations: 2x+3y-2z=0 , 2x-y+3z=0 , 7x+lambday-z=0 has non-trivial solutions.

Consider the system of equations : x sintheta-2ycostheta-az=0 , x+2y+z=0 , -x+y+z=0 , theta in R

Let lambdaa n dalpha be real. Find the set of all values of lambda for which the system of linear equations λx+(sinα)y+(cosα)z=0 , x+(sinα)y−(cosα)z=0 , −x+(sinα)y+(cosα)z=0 has a non-trivial solution.

The value of k for which the system of equations x+ky-3z=0 , 3x+ky-2z=0, 2x+3y-4z=0 has a non -trivial solution is

The set of all values of lambda for which the system of linear equations x - 2y - 2z = lambdax x + 2y + z = lambday -x -y = lambdaz has a non-trivial solution

The system of homogenous equations tx+(t+1)y+(t-1)z=0 , (t+1)x+ty+(t+2)z=0 , (t-1)x+(t+2)y+tz=0 has a non trivial solution for

Find the real values of k for which the following system of linear equations has non-trivial solutions: x-ky+z=0,kx+3y-kz=0,3x+y-z=0

Consider the system of linear equations in x , ya n dz : ""(sin3theta)x-y+z=0 , (cos2theta)x+4y+3z=0 , 2x+7y+7z=0 Which of the following can be the value of theta for which the system has a non-trivial solution (A) npi+(-1)^npi/6,AAn in Z (B) npi+(-1)^npi/3,AAn in Z (C) npi+(-1)^npi/9,AAn in Z (D)none of these

Find the real values of k for which the following system of linear equtions has non -trivial solution: x-ky-z=0,kx-y-z=0,x+y-z=0 .

Find the real values of K for which the following system of linear equations has no-trivial solution: x - ky - z = 0, kx - y - z = 0, x + y-z = 0