If the system of equations `x=c y+b z` `y=a z+c x` `z=b z+a y` has a non-trivial solution, show that `a^2+b^2+c^2+2a b c=1`

If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y has a non-trivial solution show that a^2+b^2+c^2+2a b c=1

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

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

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-c-b-c b-a-b-a c| (b) |a b c b c a c a b| |a c bb a cc b a| (d) |a a+bb+c bb+cc+a cc+a a+b|

If a!=b!=c!=1 and the system of equations ax+y+z=0,x+by+z=0 ,x+y+cz=0 have non trivial solutions then a+b+c-abc

If a,b,c are non-zero real numbers and if the system of equations (a-1)x=y+z(b-1)y=z+x(c-1)z=x+y has a non-trivial solution,then ab+bc+ca equals to (A) abc( B) a^(2)-b^(2)+c^(2)(C)a+b-c( D ) None of these

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 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