# Calculate the unknowns values that satisfy determinant of matrix equals to zero

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Hidir ABAY on 24 Dec 2016
Answered: Soumya Saxena on 28 Dec 2016
Hello everyone,
I'll try to be syntetic :
- I have a system : Mx'' +Cx' +Kx = 0 (M, C and K are matrices of size [m x n] and x a vector [mx1] - I say that x=A exp(i*w*t) (with w the pulsation and t the time) - I have (-w²M + C iw + K)A = 0
I want to find the values w (w is an unknown vector [m x 1]) that satisfy determinant (-w²M + C iw + K)=0 and I don't know if it is possible or not, and if it's possible how can I do ?
Thank you.
Star Strider on 24 Dec 2016
It seems that ‘w’ could be an eigenvalue. Explore the eig function (and its friends) to see if it will do what you want.

Soumya Saxena on 28 Dec 2016
I understand that you would like to determine the values of "w" that satisfy the equation, (-w²M + C iw + K)=0. However, in order to better understand your question and provide you with a suggestion, please provide me some more information :
1. What is your use case ? What physical system are you modelling ?
2. What is the end goal that you are trying to achieve ?
3. As mentioned in the post, (-w²M + C iw + K) is the determinant of a matrix. Could you please let me know what matrix it is and how you are defining it ?
4. Please also provide me the exact values of M, C and K, and how you are initializing them.
In general, the unknowns values that make the determinant 0 are the roots of the characteristic equation and are the eigenvalues. To calculate eigenvalues, you may use the "eig" function as given in the following documentation: