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 prove that `a b+b c+c a=a b cdot`

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

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

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 a , b , c are distinct real numbers and the system of equations a x+a^2y+(a^3+1)z=0 b x+b^2y+(b^3+1)z=0 c x+c^2y+(c^3+1)=0 has a non-trivial solution, show that a b c=-1

If a , b , c are distinct real numbers and the system of equations a x+a^2y+(a^3+1)z=0 b x+b^2y+(b^3+1)z=0 c x+c^2y+(c^3+1)=0 has a non-trivial solution, show that a 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

If the system of linear equations x=cy+bz , y=az+cx , z=bx+ay has a non trivial solution show that a^2+b^2+c^2+2abc=1

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

Prove that the system of equations in xa +y+z=0 , x +by +z=0 , x +y+cz=0 has a non - trivial solution then 1/(1-a) + 1/(1-b)+ 1/(1-c)=

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