MATLAB: How to use for loops to calculate the determinant of the first n powers of 2×2 matrix (A) without using the implicit Matlab command “det”

determinantfor loophomeworkif statment

I am allowed to use the for loop as well as if/elseif/else statements to create the function but I am not sure how exactly to do this. The input will be a matrix A and a scalar value n. I began using if statements to make sure that the matrix is 2×2 and that n is positive however i do not know how to code for det(A^n) without using the det function. Below is an example of what i have thus far:
 function ret = invertiblePowers(A,n)
   if isequal(size(A), [2 2])==0
      ret= disp('Matrix has wrong dimensions')
   elseif floor(n)~=ceil(n)
      ret= disp('n is not a positive integer')
   elseif  isequal(size(A), [2 2])==1 & floor(n)=ceil(n)

Best Answer

You're going to want a function that takes A and n as inputs and either returns a string or nothing at all. That would look like
 function ret = invertiblePowers(A,n)
or
 function [] = invertiblePowers(A,n)
Assuming you want to return a string, then just do something like
 function ret = invertiblePowers(A,n)
 ret = ''; % initialize ret to empty string
 % Make sure A is the right size
 if (~isequal(size(A),[2,2]))
  ret = 'Matrix has wrong dimensions'; % note that 'disp' is not used
  return;  % stop working and exit out of this function
 end
 % Make sure n is positive integer
 if ((floor(n)~=ceil(n)) || (n <=0))
   ret = 'n is not a positive integer';
   return;
 end
 % if A is 2x2 and n is positive integer, find det(A^n)
 % It's unclear whether this function needs to find all 
 %  determinates for I=1 up to n, or just n. 
 % Assuming you want 1:n, loop through
 for i = 1:n
   An = A^i; % raise A to the ith power
   % find the determinate here, you need to do this part
   detAn = YOUR MATH HERE;
   % append results to return string
   ret = [ret ; sprintf('n = %i : det(A^n) = %f',i,detAn)];
 end % end for loop
 end
Related Question