The system of homogenous equations
`tx+(t+1)y+(t-1)z=0`, `(t+1)x+ty+(t+2)z=0`, `(t-1)x+(t+2)y+tz=0` has a non trivial solution for

The number of real values of t such that the system of homogeneous equations tx+(t+1)y+(t-1)z=0, (t+1)x+ty+(t+2)z=0,(t-1)x+(t-2)y+tz=0 has non trivial solutions is

If the system of homogeneous equations tx+(t+1)y+(t-1)z=0 (t+1)x+ty+(t+2)z=0 (t-1)x+(t+2)y+tz=0 in x,y,z has a non-trivial solution, then t is a root of the equation

if the system of equations (a-t)x+by +cz=0 bx+(c-t) y+az=0 cx+ay+(b-t)z=0 has non-trivial solutions then product of all possible values of t is

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

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 System is always non trivial solutions System is consistent only when a=b=c If a!=b!=c then x=0,\ y=t ,\ z=-t\ AAt in R 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

The equation x =1/2 (t+ (1)/(t)), y = 1/2 (t - 1/t), t ne 0 represents

The equation x =1/2 (t+ (1)/(t)), y = 1/2 (t - 1/t), t ne 0 represents