If $f(x)=\left|\begin{array}{ccc}x+\lambda & x & x \ x & x+\lambda & x \ x & x & x+\lambda\end{arr

Question

If $f(x)=\left|\begin{array}{ccc}x+\lambda & x & x \ x & x+\lambda & x \ x & x & x+\lambda\end{array}ight|$, then $f(3 x)-f(x)$ is equal to

Professor PC Thomas Classes · Answer

Evaluating determinant gives $f(x) = \lambda^2 (3x+\lambda)$. Thus $f(3x) - f(x) = \lambda^2(9x+\lambda - 3x - \lambda) = 6x\lambda^2$.