Ifthe equations `a(y +z) =x,b(z+x) = y, c (x + y) = z` have nontrivial solutions, then `1/(1+a)+1/(1+b)+1/(1+c)=`

a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y+z=0,a n dx+y+c z=0 have nontrivial solution, then the value of 1/(1-a)+1/(1-b)+()/(1-c) is equal to a.1 b. -1 c.z e ro d. none of these

If the system of linear equations a(y+z)-x=0,b(z+x)-y=0,c(x+y)-z=0 has a non trivial solution,(a!=-1,b!=-1,c!=-1), then show that (1)/(1+a)+(1)/(1+b)+(1)/(1+c)=2

If a, b and c are non - zero real numbers and if system of equations (a-1)x=y+z, (b-1)y=z+x and (c-1)z=x+y have a non - trivial solutin, then (3)/(2a)+(3)/(2b)+(3)/(2c) is equal to

if the system of equation ax+y+z=0,x+by=z=0, and x+y+cz=0(a,b,c!=1) has a nontrival solution,then the value of (1)/(1-a)+(1)/(1-b)+(1)/(1-c)is:

If the system of equation x=a(y+z),y=b(z+x),z=c(x+y),(a,b,c!=-1) has a non-zero solution then the value of (a)/(a+1)+(b)/(b+1)+(c)/(c+1) is

The value of a such that the system of equations x-2y+z=-4, 2x – y +2z = 2 and x+y+az = 4, has no solution , is a) 0 b)1 c)3 d)-1

If x,y,z not all zeros and equations x+y+z=0,(1+a)x+(2+a)y-8z=0,x-(1+a)y+(2+a)z= have non trivial solution then a