Evaluate the following: ` |[x+lamda, x, x],[x, x+lamda, x],[x, x, x+lamda]| `

Evaluate the following determinant abs((x+lamda,x,x),(x,x+lamda,x),(x,x,x+lamda))

Evaluate |(x+lamda,x,x),(x,x+lamda,x),(x,x,x+lamda)|

Using Properties of determinants, prove that {:|(x+lamda,2x,2x),(2x,x+lamda,2x),(2x,2x,x+lamda)|=(5x+lamda)(lamda-x)^2

If f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =

If f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =

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

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