[" C.6."|f" a,"b," care non zeros,then the system of equations "],[qquad [(alpha+a)x+ay+az=0],[alpha x+(alpha+b)y+az=0],[alpha x+ay+(alpha+c)z=0]],[" has a non-trivial solution it "]

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0, alphax+(alpha+b)y+alphaz=0, alphax+alphay+(alpha+c)z=0 has a non-trivial solution if

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0, alphax+(alpha+b)y+alphaz=0, alphax+alphay+(alpha+c)z=0 has a non-trivial solution if

If a,b,are non-zeroes then the system of equations (alpha+a)x+alpha y+alpha z=0alpha x+(alpha+b)y+alpha z=0alpha x+alpha y+(alpha+c)z=0

If a,b,c are non-zero,then the system of equations (alpha+a)x+alpha y+alpha z=0,alpha x+(alpha+b)y+alpha z=0,alpha x+alpha y+(alpha+c)z=0 has a non-trivial solution if alpha^(-1)=(A)-(a^(-1)+b^(-1)+c^(-1))(B)a+b+c (C) alpha+a+b+c=1 (D) none of these

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0,alphax+(alpha+b)y+alphaz=0,alphax+alphay+(alpha+c)z=0' has a non-trivial solution if alpha^(-1)= (A) -(a^(-1)+b^(-1)+c^(-1)) (B) a+b+c (C) alpha+a+b+c=1 (D) none of these

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0,alphax+(alpha+b)y+alphaz=0,alphax+alphay+(alpha+c)z=0' has a non-trivial solution if alpha^(-1)= (A) -(a^(-1)+b^(-1)+c^(-1)) (B) a+b+c (C) alpha+a+b+c=1 (D) none of these

If a , b , c are non-zero, then the system of equations (alpha+a)x+alphay+alphaz=0,alphax+ , (alpha+b)y+alphaz=0,alphax+alphay+(alpha+c)z=0 has a non-trivial solution if alpha^(-1)= (A) -(a^(-1)+b^(-1)+c^(-1)) (B) a+b+c (C) alpha+a+b+c=1 (D) none of these

The system of equations alpha x + y + z = alpha - 1 x + alpha y + = alpha - 1 , x + y + alpha z = alpha - 1 has infinite solutions, if alpha is