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`

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 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 , 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 c

If the system of equations x=cy+bz, y=az+cx and z=bx+ay has non-trivial solution and at least one of a,b, c is a proper fraction, prove that a^(2)+b^(2)+c^(2) lt 3 and abc gt -1

If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy + cz =0 has a non-zero solution, then a, b, c

If the system of equations bx + ay = c, cx + az = b, cy + bz = a has a unique solution, then

The greatest value of for which the system of linear equations x-cy-cz=0 cx-y+cz=0 cx+cy-z=0 Has a non-trivial solution, is 1/k . The value of k is _________.

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 linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y+c z=0 has a non zero solution then (a) System is always non trivial solutions (b) System is consistent only when a=b=c (c) If a!=b!=c then x=0,\ y=t ,\ z=-t\ AAt in R (d) If a=b=c\ t h e n\ y=t_1, z=t_2,\ x=-a(t_1+t_2)AAt_1, t_2 in R

Given that the system of equations x=cy+bz ,y=az+cx , z=bx +ay has nonzero solutions and and at least one of the a,b,c is a proper fraction. a^(2)+b^(2)+c^(2) is