Why doesn't the minor matrix match?

Please check my script

I'm working on an assignment to find the determinant using minor. I'm confused why minor doesn't match with the result, so that the final result is not same as the original determinant

syms L
disp('----------------------------------------------------------------');
% Use minors to expand the above determinant:
A = [2-L 8 10;8 4-L 5;10 5 7-L]; 
disp(A)
disp('x is lambda');
disp('----------------------------------------------------------------');
M11 = A([2,3],[2,3]) 
M12 = A([2,1],[2,3]) 
M13 = A([2,1],[2,2]) 
DM = A(1,1)*det(M11)-A(1,2)*det(M12)+A(1,3)*det(M13)
det(M11)
det(A)

please help me

Answer 1

[Cris LaPierre]

It looks like you have not correctly implemented the expansion of minors. Check your M arrays.

[Jaemon Hon]

I managed to make a minor like this

M11 = A(2:3,[2,3]) 
M12 = A(2:3,[1,3]) 
M13 = A(2:3,[1,2]) 

and it worked

but, I don't know why the result didn't immediately calculate like this

- L^3 + 13*L^2 + 139*L - 42

on Command Window appears like this

DM = 164*L - (L - 2)*(L^2 - 11*L + 3) - 48

[Cris LaPierre]

MATLAB doesn't "know" how you want it to appear. It provided an equivalent solution.

Add this after you compute DM.

simplify(DM)

[Jaemon Hon]

I did it, thank you very much sir