Symbolic question

[FrenchLeaf]

Hello,

I want to resolve the following problem :

Det(alpha*F1 +(1 - alpha)*F2) == a3*lambda + a2*lambda + a1 *lambda +a0 = 0

F1 and F2 are 3*3 matrix. Alpha is a single value.
The problem is from the formula of the right of I can obtain the a3,a2,a1,a0
factor to compute the lambda roots.

I know that is feasible in Maple, but I do not know How, and I did not have
maple...

I have test to find the solution with Xcas (solve), but Xcas seems cannot
handle it.

I have start with the following idea :
f = det( (alpha* [ [a1,b1,c1] , [d1,e1,f1] ,  [g1,h1,i1] ]) * ( (1-alpha) *
[ [a2,b2,c2] , [d2,e2,f2] ,  [g2,h2,i2] ] ) );
g = a3*lambda + a2*lambda + a1 *lambda +a0;

=> How to try to solve the system to identify the three A factor now ?

Thanks in advance for your suggestion ;)
Pierre.
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