Help with nxn matrices

I am having a bit of trouble with an nxn matrix problem.

The problem is: Write a user-defined MATLAB function that calculates the determinant of a square ( _n x n _ ) matrix, where n can be 2, 3, or 4. For function name and arguments, use D= Determinant(A). The input argument A is the matrix whose determinant is calculate. The function Determinant show first check if the matrix is a square. If it is not, the output D should be the message "The matrix must be square." Use Determinant to calculate the determinant of the following matrices.

It then goes on to give two different matrices, however, that is not what I need help with. My function is what is giving me difficulties. I entered the 3x3 matrix that I was given first, and came up with an error in the 34th line of my code saying that it was incomplete or incorrect. I have italicized this line to make it easier to find. Any help is greatly appreciated. Thank you!

Here is my code:

function D = Determinant( A )
% The function calculates the determinant of an nxn matrix A,
% where n can be 2, 3, or 4.

[n m]=size(A);  % n= # of rows in A, m= # of columns in A

if n ~= m    % check if A is a square matrix
d ='ERROR'    % if not, display error message
disp('The matrix has to be square')

elseif n > 4  % otherwise, check if A is larger than 4x4
d ='ERROR'    % if so, display error message
disp('The matrix size cannot be larger than 4 by 4')

elseif n == 2  % otherwise, check if A is 2x2
D=det2by2(A);  % if so, call the subfunction for a 2x2 determinant

elseif n == 3  % otherwise, check if A is 3x3
D=det3by3(A);  % if so, call the subfunction for a 3x3 determinant

elseif n == 4  % otherwise, check if A is 4x4
D=det4by4(A);  % if so, call the subfunction for a 4x4 determinant

end      % end the program
%Subfunctions

function D4 = det4by4( A )
% The function calculates the determinant of a 4 by 4 matrix.
Sa=A(2:4,2:4);
Sb=A(2:4,[1 3 4]);
Sc=A(2:4,[1 2 4]);
Sd=A(2:4,1:3);

%
_D4=A(1,1)*det3by3(Sa)-A(1,2)*det3by3(Sb)+A(1,3)*det3by3(Sc)-

A(1,4)*det3by3(Sd);_
%
function d3=det3by3(A)

%
% Evaluating the determinant by expanding using the first row

%
S1=A(2:3,2:3);
%
S2=A(2:3,[1 3]);
%
S3=A(2:3,1:2);
%
d3=A(1,1)*det2by2(S1)-A(1,2)*det2by2(S2)+A(1,3)*det2by2(S3);

%
% Subfunction
%
function d2=det2by2(B)
d2=B(1,1)*B(2,2)-B(1,2)*B(2,1);

end
end

[Claire]

Part of the code got bunched up at the end. It should look like this:

 _D4=A(1,1)*det3by3(Sa)-A(1,2)*det3by3(Sb)+A(1,3)*det3by3(Sc)-

A(1,4)*det3by3(Sd);_

 function d3=det3by3(A)

 % Evaluating the determinant by expanding using the first row

 S1=A(2:3,2:3); 
 S2=A(2:3,[1 3]); 
 S3=A(2:3,1:2); 
d3=A(1,1)*det2by2(S1)-A(1,2)*det2by2(S2)+A(1,3)*det2by2(S3);

 % Subfunction % function 
d2=det2by2(B) d2=B(1,1)*B(2,2)-B(1,2)*B(2,1);

[Claire]

The line starting with D4=A(1,1)*det3by3(Sa)... is the line that I am having trouble with.

[Star Strider]

To format your code, highlight it, then use the [{}Code] button. Alternatively, put two spaces between the left window margin and each line of your code.

[Claire]

Thank you. I will definitely do that in the future.

Answer 1

[per isakson]

The only problem I find is the two ending end. After adding end to the end of each function. (You don't say what kind of trouble you see.)

    >> A = rand(4);
    >> det(A)
    ans =
       -0.0261
    >> D = Determinant( A )
    D =
    -0.0261

&nbsp

Addendum in response to comment.

    >> A=[1 5 4; 2 3 6; 1 1 1]
    >> D = Determinant( A )
    D =
        13
    >> det(A)
    ans =
        13
    >>

where my version of your function, Determinant, is attached. I have added an end to the end of each function. Either all functions should be closed with end or none.

[Claire]

Line 34,

D4=A(1,1)*det3by3(Sa)-A(1,2)*det3by3(Sb)+A(1,3)*det3by3(Sc)-A(1,4)*det3by3(Sd)

gives me an error each time I run it saying "Expression or statement is incomplete or incorrect".

The actual matrix I have to enter is:

A=[1 5 4; 2 3 6; 1 1 1]

[per isakson]

The line looks ok to me. I think your problem has something to do with missing or surplus end. I added your example to my answer.

[Claire]

Yes! Thank you very much. It worked perfectly now.

Answer 2

[Iboi Lucky]

Nice job! Can I please get a similar code that would solve determinant above 4 x 4 matrix please!!

[Steven Lord]

If this is not a homework assignment, read the Limitations section on the documentation page for the det function. Unless you absolutely positively need the determinant and understand those limitations, use cond or rcond instead. If you do absolutely need the determinant, call det.

If this is a homework assignment, your textbook probably has some pseudocode that you can implement in MATLAB. If not, you could use the idea shown at the start of the Wikipedia article for the determinant to write the determinant of an n-by-n matrix as sums of multiples of the determinants of n (n-1)-by-(n-1) matrices.

[Iboi Lucky]

It's actually my project work, my supervisor asked me to write a code that would solve n by n determinant which is actually my project topic and to be honest, I can't seem to find it anywhere online.