I want to find the determinant for 5.5 matrix

I need to find the determinant in symbol s1 to s10 (without values). Here the matrix M:

M=[0 -s1 -s2 -s3 -s4; s1 0 -s5 -s6 -s4; s2 s5 0 -s8 -s9; s3 s6 s8 0 -s10; s4 s7 s9 s10 0];

Many thanks.

Answer 1

[Walter Roberson]

>> syms s1 s2 s3 s4 s5 s6 s7 s8 s9 s10
>> M = [0 -s1 -s2 -s3 -s4; s1 0 -s5 -s6 -s4; s2 s5 0 -s8 -s9; s3 s6 s8 0 -s10; s4 s7 s9 s10 0];
>> det(M)
ans =
s1*s4^2*s8^2 - s1*s4*s7*s8^2 - s2*s4^2*s6*s8 + s3*s4^2*s5*s8 - s3^2*s4*s5*s9 - s2^2*s4*s6*s10 + s3^2*s5*s7*s9 + s2^2*s6*s7*s10 + s2*s3*s4*s5*s10 + s2*s3*s4*s6*s9 + s1*s2*s4*s8*s10 - s1*s3*s4*s8*s9 - s2*s3*s5*s7*s10 - s2*s3*s6*s7*s9 + s2*s4*s6*s7*s8 - s3*s4*s5*s7*s8 - s1*s2*s7*s8*s10 + s1*s3*s7*s8*s9
>> simplify(ans)
ans =
(s4 - s7)*(s3*s5 - s2*s6 + s1*s8)*(s2*s10 - s3*s9 + s4*s8)

Answer 2

[KSSV]

clc; clear all ;
syms s1 s2 s3 s4
A = [s1 s2 ; s3 s4] ;
det(A)

The above shows determinant for 2x2 matrix. you may extend it for your matrix.