# The generalized Eigen value problem [K- λM]X=0 has a non-zero solution for X. What is the value of λ if K=$\begin{pmatrix}1&1&1\\1&1&1\\1&1&1\end{pmatrix}$, M=$\begin{pmatrix}4&4&4\\4&4&4\\4&4&4\end{pmatrix}$?

The generalized Eigen value problem [K- λM]X=0 has a non-zero solution for X. What is the value of λ if K=$\begin{pmatrix}1&1&1\\1&1&1\\1&1&1\end{pmatrix}$, M=$\begin{pmatrix}4&4&4\\4&4&4\\4&4&4\end{pmatrix}$?

(a) 1

(b) $\frac{1}{2}$

(c) 4

(d) $\frac{1}{4}$

I got this question in an interview for internship.

My doubt stems from Eigen Value and Time Dependent Problems in chapter Single Variable Problems of Finite Element Method

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The correct option is (d) $\frac{1}{4}$

The best explanation: The generalized Eigen value problem [K- λM]X=0 has a non-zero solution for X if the determinant of the matrix [K- λM] equals zero or K=λM

$\begin{pmatrix}1&1&1\\1&1&1\\1&1&1\end{pmatrix}$=λ$\begin{pmatrix}4&4&4\\4&4&4\\4&4&4\end{pmatrix}$

Equating corresponding elements, we get 1=4*λ

λ=$\frac{1}{4}$.

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