Creating a function that calculates the determinant and inverse of a 3x3 matrix

I need to create a function that calculates the determinant and the inverse of a generic 3 X 3 matrix with the method of the cofactors and the adjoint matrix. The function has to calculate the determinant using the cofactors. If the determinant is zero, the inverse is set to be an empty matrix. If the determinant is non-zero, then it calculates the inverse according to the algorithm. I also have to use the function "invanddet2by2sol".

I don't understand how to use that invanddet2by2sol function, i.e. where to put it. so far I have this code

    function [ determinant, inverse ] = invanddet3by3( A )
  %INVANDDET3BY3 Calculates the determinant and the inverse of a 3 X 3 matrix by using 
  % cofactors and adjoint matrix
      A11 = invanddet2bysol([A(2,2), A(2,3); A(3,2), A(3,3)]); % Cofactors 3x3 matrix A
      A12 = -(invanddet2by2sol([A(2,1), A(2,3); A(3,1), A(3,3)]));
      A13 = invanddet2by2sol([A(2,1), A(2,2); A(3,1), A(3,2)]);
      A21 = -(invanddet2by2sol([A(1,2), A(1,3); A(3,2), A(3,3)]));
      A22 = invanddet2by2sol([A(1,1), A(1,3); A(3,1), A(3,3)]);
      A23 = -(invanddet2by2sol([A(1,1), A(1,2); A(3,1), A(3,2)]));
      A31 = invanddet2by2sol([A(1,2), A(1,3); A(2,2), A(2,3)]);
      A32 = -(invanddet2by2sol([A(1,1), A(1,3); A(2,1), A(2,3)]));
      A33 = invanddet2by2sol([A(1,1), A(1,2); A(2,1), A(2,2)]);
  J = [ A11 A12 A13; A21 A22 A23; A31 A32 A33]; % Adjugate Matrix
  determinant = ((A(1,1) * A11) + (A(1,2) * A12) + (A(1,3) * A13)); % Determinant of A
  inverse = (1/determinant) * (J'); % Inverse of A
  if determinant==0
  inverse=[];
  end

[Walter Roberson]

It appears to be already in invanddet2by2sol.m which is all that is needed provided it is on your search path.

[Tai Lopez]

Yes, it is on my search path. When I create a random 3x3 matrix and type "invanddet3by3( A )" in the command window and press enter, it just says "undefined function". Do you know what is wrong because I should be getting a determinant and an inverse?

[Walter Roberson]

Is it saying that invanddet3by3 is undefined, or is it saying that invanddet2by2sol is undefined?

[Tai Lopez]

invanddet3by3 is undefined

Answer 1

[Walter Roberson]

Your code invokes

        A11 = invanddet2bysol([A(2,2), A(2,3); A(3,2), A(3,3)]); % Cofactors 3x3 matrix A

which uses invanddet2bysol instead of invanddet2by2sol

[Tai Lopez]

yes, sorry, my bad. I've been playing around with the code and accidentally deleted the "2". It has now been corrected but the function is still undefined.

[Walter Roberson]

Please show the output of

which -all invanddet3by3
pwd
ls

I notice in your image that your file name is Untitled and that it is not saved to disk. You would need to Save that editor window; it will ask you what filename to save to and it would suggest invanddet3by3.m as the name, which is what you should use.