Home
Class 12
MATHS
The system of equations lambdax+y+z=0 ,...

The system of equations `lambdax+y+z=0` , `-x+lambday+z=0` and `-x-y+lambdaz =0` will have a non-zero solution , if real values of `lambda` are given by

A

`lambda=1`

B

`lambda=0`

C

`lambda=-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

The system of linear equations x+lambday-z=0 , lambdax-y-z=0 , x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

A system of equations lambdax +y +z =1,x+lambday+z=lambda, x + y + lambdaz = lambda^2 have no solution then value of lambda is

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.

Find a in R for which the system of equations 2ax-2y+3z=0 , x+ay + 2z=0 and 2x+az=0 also have a non-trivial solution.

x+ky-z=0 , 3x-ky-z=0 and x-3y+z=0 has non-zero solution for k=

The set of all values of lambda for which the system of linear equations: x-2y-2z=lambdax , x+2y+z=lambday and -x-y=lambdaz has a non-trivial solution: (a) is an empty sheet (b) is a singleton (c) contains more than two elements (d) contains exactly two elements

The system of equations ax + 4y + z = 0,bx + 3y + z = 0, cx + 2y + z = 0 has non-trivial solution if a, b, c are in

If the system of equations 3x-2y+z=0, lambda x-14y+15z=0, x+2y+3z=0 have a non trivial solution, then the value of lambda^(2) must be

If 4x-ay+3z=0, x+2y+az=0 and ax+2z=0 have a non - trivial solution, then the number of real value(s) of a is