If x,y,z not all zeros and equations `x+y+z=0, (1+a)x +(2+a)y -8z =0, x- (1+a)y + (2+a)z =0` have non trivial solution then a

If the following equations x+y-3z = 0, (1+lamda)x + (2+lamda) y - 8z = 0, x-(1+lamda)y + (2+lamda)z = 0 are consistent then the value of lamda is

If the following equations x+y-3z = 0, (1+lamda)x + (2+lamda) y - 8z = 0, x-(1+lamda)y + (2+lamda)z = 0 are consistent then the value of lamda is

Show that the homogenous system of equations x - 2y + z = 0, x + y - z = 0, 3 x + 6y - 5z = 0 has a non-trivial solution. Also find the solution

The system of linear equations x + lambda y-z =0, lambdax-y -z =0, x + y -lambda z =0 has a non-trivial solution for

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 the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y+z = 0 has a non-trivial solution (x, y, z), then (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y+z = 0 has a non-trivial solution (x, y, z), then (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

If the equations x = ay +z, y = az+x and z = ax + y+(ane0) are consistent having a non-trivial solution, then a^2 +3= ....