The values of `lamda` for which the system of equations `x+y-3=0, (1+ lamda)x+(2+lamda)y-8=0, x-(1+lamda)y+(2+lamda)=0` is consistent are

The values of lamda for which the system of equations x+y-3=0 (1+lamda)x+(2+lamda)y-8=0 x-(1+lamda)y+(2+lamda)=0 has a non trivial solution are

The number of distinct real values of lamda for which the system of linear equations x + y + z = lamda x , x + y + z = lamday, x + y + z + lamda z has non - trival solution.

The number of distinct real values of lamda for which the system of linear equations x + y + z = lamda x , x + y + z = lamday, x + y + z + lamda z has non - trival solution.

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-3 = 0, (1+lamda)x + (2+lamda) y - 8 = 0, x-(1+lamda)y + (2+lamda) = 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

The values of lamda for which one root of the equation x^2+(1-2lamda)x+(lamda^2-lamda-2)=0 is greater than 3 and the other smaller than 2 are given by