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

The system of linear equations
x + y + z = 0
`(2x)/(a) + (3y)/(b) + (4z)/(c ) = 0`
`(x)/(a) + (y)/(b) + (z)/(c ) = 0`
has non trivia solution then

A

a + b + c = 0

B

a, b, c are in GP

C

`(1)/(a), (1)/(b), (1)/(c )` are in AP

D

a,b,c are in AP

Text Solution

Verified by Experts

The correct Answer is:
D
`|{:(1,1,1),((2)/(a),(3)/(b),(4)/(c )),((1)/(a),(1)/(b),(1)/(c )):} |`
`1((3)/(bc) - (4)/(bc)) - 1 ((2)/(ac) - (4)/(ac)) + 1 ((2)/(ab) - (3)/(ab)) = 0`
`- (1)/(bc) + (2)/(ac) - (1)/(ab) = 0` `implies` -a + 2b - c = 0 `implies` a,b,c are in AP
Promotional Banner

Similar Questions

Explore conceptually related problems

What should be the value of k so that the system of linear equations x - y + 2z = 0, kx - y + z = 0, 3x + y - 3z = 0 does not possess a unique solution ?

What should be the value of k so that the system of linear equations x - y + 2z = 0, kx - y + z = 0, 3x + y - 3z = 0 does not possess a unique solution ?

If the system of linear equations x + y + 3z = 0 x + 3y + k^2 z = 0 3x + y + 3z = 0 has a non -zero solution (x, y, -z) for some k in R then x + (y/z) is equal to :

The system of linear equations x - 2y + z = 4 2x + 3y - 4z = 1 x - 9y + (2a + 3)z = 5a + 1 has infinitely many solution for:

The system of equations -2x+y+z=a x-2y+z=b x+y-2z=c has

The value of a for which the system of equations , a^(3)x + (a + 1)^(3) y + (a + 2)^(3) z = 0 , ax + (a + 1) y + (a + 2) z = 0 & x+y+z=0 has a non - zero solution is :

If the system of linear equations 2x + 2y +3z =a 3x - y +5z =b x- 3y +2z =c where a, b, c are non-zero real numbers, has more than one solution, then