Mathematics - Determinant Question with Solution | TestHub

On solving, we get:

$$\begin{array}{rl}(2\lambda +15)f(x+1)-(\lambda +10)f(x+8)-f(x+1)& =0\\ (2\lambda +14)f(x+1)& =(\lambda +10)f(x+8)\end{array}$$

Since $f$ is periodic with period 7,

$$\begin{array}{rl}\therefore f(x+1)& =f(x+8)\\ \Rightarrow 2\lambda +14& =\lambda +10\\ \Rightarrow \lambda & =-4\\ \Rightarrow |\lambda |& =4Ans.\end{array}$$