Home
Class 12
MATHS
The system of equations alphax+y+z=a...

The system of equations
`alphax+y+z=alpha-1,`
`x+alphay+z=alpha-1`
`x+y+alphaz=alpha-1`
and has no solution if `alpha` is

A

not -2

B

1

C

-2

D

Either -2 or 1

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

The system of equations ax-y- z=a-1 ,x-ay-z=a-1,x-y-az=a-1 has no solution if a is

The system of equations x+2y-4z=3,2x-3y+2z=5 and x -12y +16z =1 has

Knowledge Check

  • The system of equations ax+y+z=a-1,x+ay+z=a-1andx+y+az=a-1 does not have unique solution if a = ……..

    A
    1 or -2
    B
    3
    C
    2
    D
    `-1`
  • Similar Questions

    Explore conceptually related problems

    Statement I The system of linear equations x+(sin alpha )y+(cos alpha )z=0 x+(cos alpha ) y+(sin alpha )z=0 -x+(sin alpha )y-(cos alpha )z=0 has a not trivial solution for only one value of alpha lying between 0 and pi . Statement II |{:(sin x, cos x , cos x),( cos x , sin x , cos x) , (cos x , cos x , sin x ):}|=0 has no solution in the interval -pi//4 lt x lt pi//4 .

    Let lambda "and" alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+(sinalpha)y+(cos alpha)z=0 x+(cos alpha) y+(sin alpha) z=0 -x+ (sin alpha) y-(cos alpha) z=0 has a non- trivial solution then S contains

    If the system of equations x + 2y + 3z = 4, x+ py+ 2z = 3, x+ 4y + z = 3 has an infinite number of solutions and solution triplet is

    If sin 3 alpha =4 sin alpha sin (x+alpha ) sin(x-alpha ) , then

    Let alpha_1,alpha_2a n d\ beta_1,beta_2 be the roots of a x^2+c=0\ a n d\ p x^2+q x+r=0 respectively. If the system of equations alpha_1, y+alpha_2z=0\ a n d\ beta_1y+beta_2z=0 has anon-trivial solution, then prove that (b^2)/(q^2)=(a c)/(p r)dot

    Transform the equation y = x tan alpha to polar form.

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