Home
Class 12
MATHS
The system of linear equations x+lambd...

The system of linear equations
`x+lambday-z=0`
`lambdax-y-z=0`
`x+y-lambdaz=0`
has a non-trivial solution for

A

infinitely many values of `lambda`

B

exactly one value of `lambda`

C

exactly two values of `lambda`

D

exactly three values of `lambda`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE ADVANCED ARCHIVE 2013|2 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE ADVANCED ARCHIVE 2014|2 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE MAIN (AIEEE) ARCHIVE 2015|2 Videos

  • ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

  • ARCHIVE

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|13 Videos

Similar Questions

Explore conceptually related problems

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 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

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.

Find the number of values of lambda for which the system of equations lambdax+y+z=1,x+lambday+z=lambda and x+y+lambdaz=lambda^2 has infinite number of solutions .

Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+lambday+(c-b)z=0,a n d(a-c)x+(b-c)y+lambdaz=0 has a non trivial solution, then the value of lambda is 0. Statement 2: the value of skew symmetric matrix of order 3 is Zero.

If the system of linear equations x+ky+3z=0; 3x+ky-2z=0; 2x+4y-3z=0 has a non-zero solution (x,y,z) then (xz)/(y^2) is equal to

If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy + cz =0 has a non-zero solution, then a, b, c

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is (a) |[a, -c, -b], [-c, b, -a], [-b, -a, c]| (b) |[a, b, c], [b, c, a], [c, a, b]| (c) |[a, c, b], [b, a, c], [c, b, a]| (d) |[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|

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.