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in Finite Element Method by (110k points)
A generalized Eigen value problem [K- ω^2M]X=0 has a non-zero solution for X. What can be the value of determinant of the matrix [K- ω^2M]?

(a) Any integer

(b) 0

(c) +1

(d) Positive integer

I had been asked this question in a national level competition.

Enquiry is from Eigen Value and Time Dependent Problems topic in division Single Variable Problems of Finite Element Method

1 Answer

+2 votes
by (185k points)
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Best answer
Right choice is (b) 0

Explanation: A generalized Eigen value problem is represented by homogeneous matrix equation, [K- ω^2M]X=0. From matrix equations methods, the equation has a non-zero solution for X if the determinant of the matrix [K-ω^2M] equals to zero.

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