could u send the file

Thanks you again that really helps.

Hello i have another question, in addition to this how do we ask maple to automatically find the eigenvalues and eigenvectors of these matrices?

Thanks again

ohhh excellent thats exactly what i wanted

thank you very much

and just to add to that, we choose four of the eight roots, thats why there are four m's, i.e, m1 m2 m3 m4, and not m1 m2...m7 m8.

Thanks,

oh thank you, very simple.

m[1] etc are the roots of the eighth order equation in m. For example ax^2 + bx + c gives two roots, x[1] and x[2].

Thank you,

Hi i think you have misunderstood  me. Because for each lambda we should get eight roots of m. But solve({eqn1,eqn2}) doesnt give this. furthermore, the lambda value(s) should satisfy the determinant of the boundary conditions to be zero ( the last matrix in the file i attached previously), and for this we do need the eigen vectors as well.

Please explain more.

Thank you so much.

Alright I attached the maple file for my problem. I hope that the steps and writing is clear enough.View 11295_TEST1.mw on MapleNet or Download 11295_TEST1.mw
View file details

Yes sorry i meant non unique, we should arrive at a set of values.

However there are two parameters, r and x.  The roots, r, need to be substituted into the boundary conditions, and the determinant of the linear system must be equal to zero. to find the roots of r i need to solve the fourth order equation involving r and x. but the problem is that it can only be solved numerically. So i need to setup some way that maple trys values of x that give the roots of r which satisfy the determinant.

Is this understandable?

Thanks,

Thanks for that help, I understand what you have done there. However, I am dealing with a determinant of a 4x4 matrix, and the value i need to find comes from the roots of a fourth order equation which cant be solved analytically.

So for example i have ar^4 + br^3+cr^2 + dr + e=0, where there are four roots, r, and a,b,c,d,e are functions of x. I need to find the value(s) of x that satisfies this equation and the boundary conditions as well. the boundary conditions form the 4x4 matrix, and the determinant=0 shows unique solution.

Thanks and if you need more explaination let me know. I didnt put the equations here because they are very long.

Thank you ill have a look at it and let you know.