Determinant of a Matrix Without Built in Functions

I'm tasked with finding the determinant of an arbitrarily sized matrix entered by the user without using the det function. The only hint I have have been given was to use for loops. I am completely at a loss.

I started with making sure that the matrix was square:

 a1 = input ('Please input your square matrix\n');

        [nr1, nc1] = size(a1); % Creating a vector so I can check size of input
        if nr1==nc1 % Checking the matrix is square
            A = MyDet(a1); % Sending matrix to a different function
        else
            if nr1 ~= nc1 % Else for if matrix is not square
                disp('The matrix is not square, please try again')
                break % Break to stop the infinite loop
            end
         end

But now I don't know where to start with my new function MyDet. Any suggestions are helpful, thank you.

[Geoff Hayes]

Joshua - what method/algorithm have you discussed in class have for finding the determinant of a matrix?

[Joshua]

For 2*2 and 3*3 we were just taught the patterns. For 4*4 we have used cofactor expansion. 5*5 and up I am actually not sure.

Answer 1

[Matt J]

Hint: Use cofactor expansion, calling MyDet recursively to compute the cofactors.

[Joshua]

I thought because recursive functions create more functions they were an inefficient way to go about a task? Or is this is case where it is just simpler to do so?

[Matt J]

When I say "call recursively", I mean that you can make MyDet call itself. To get the idea, you can study the example below. It is a function MySum, which calls itself recursively to obtain the sum of the elements x(i) in a vector x.

    function out=MySum(x)

      if isscalar(x)
         out=x; 
      else
         out=x(1)+MySum(x(2:end));
      end

[Matt J]

I thought because recursive functions create more functions they were an inefficient way to go about a task?

Even though recursion is often inefficient, this is a homework problem where you haven't been given any requirements on efficiency (that you've mentioned). If efficiency mattered, you would be told to use builtin functions.