I want to solve a determinant of a matrix having polynomials as elements

Suppose I have a matrix A[6x6].I it have elements with 'x' as variable like A(1,1)=x^2-3 , A(1,2)=5*x^3-2*x^3+3 etc. So how should I solve these?? When I tried syms x for all writing all elements,it said inside a matrix only double should be used. My ultimate aim is to solving det(A)=0; and those polynomials are very big(solutions of sextic equation).

someone please help me

Answer 1

[John D'Errico]

No. YOU CAN use symbolic terms in a matrix. Why not show what you have tried?

syms x
A = [x^2 , 2;x, (x+1)^3];
vpasolve(det(A) == 0)
ans =
                                                                   -2.0
                                                                      0
                                     0.54368901269207636157085597180175
- 0.77184450634603818078542798590087 - 1.115142508039937359745764636315i
- 0.77184450634603818078542798590087 + 1.115142508039937359745764636315i

No problems, so I could only make wild conjectures about what you might have done wrong.

Note that an exact solution will be impossible to achieve in general, since your problem will be of too high a polynomial order.

[dipin nair]

• _ * _ _ thanks for your answer :D__*_*

clear all
clc 
syms y
a=1;
b=3;

% x=solve('a*x^2+b*x+y') I got sulution using this.But roots() is not working with a sym inside

x =[-(b + (b^2 - 4*a*y)^(1/2))/(2*a);-(b - (b^2 - 4*a*y)^(1/2))/(2*a)];

%I want to make a matrix of A=[x(1) x(2);x(1)^2 x(2)^2] I can't write directly.So I used loop as below 

for i=1:2
    A(1,i)=x(i); 
    A(1,i)=x(i)^2;
end    
vpasolve(det(A) == 0)

Answer 2

[Walter Roberson]

A = [x, x.^2].';