# How Can I Pull A Specific Variable From The Determinant of Matrix?

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Mehmet Emin Sayan on 2 Dec 2020
Answered: Walter Roberson on 2 Dec 2020
I have a huge 6x6 matrix (Matrix H) . It has 2 variable Lambda1 and Lambda2. I must pull lambda1 or lambda2. So I must write in terms of each other.
Therefore, I took determinant of matrix and equaled to zero.with,
DH=det(H)==0
And ı have a solution. Then, if I write this command to pull any Lambda
solve(DH,lambda1)
Matlab give error, like that
Warning: Unable to find explicit solution. For see help.
Empty sym : 0-by-1
What should I do ?

#### 1 Comment

Stephan on 2 Dec 2020
In some cases when solve doesnt work, isolate is able to do the job.

Ameer Hamza on 2 Dec 2020
This shows that MATLAB could not find a closed-form expression to write lambda1 in terms of lambda2. Your equation is nonlinear and for such equations, writing one variable in term of other is not always possible.

Walter Roberson on 2 Dec 2020
You have no realistic chance of calculating one variable in terms of the other symbolically. Your function involves the first two bessel functions of the first kind and the first two bessel functions of the second kind. There is no closed form solution even just to solving x=J0(y)