MuPAD Pro Computing Essentials - Examples 

Example 13.3 Cramer's Rule

This is the example demonstrating how the Cramer's rule works.

• export(linalg, nrows, ncols, delRow, delCol, det):

• minor := proc(A, i, j)
     local B;
  begin
     B := delRow(A,i);
     B := delCol(B,j);
     return(hold(Det)(B))
  end:

• Det := proc(A)
  
  begin
     r := 0;
     if (nrows(A) <> ncols(A)) then
        return("Wrong input matrix")
     else
        if nrows(A)=1 then
           return(A[1,1])
        else
           for j from 1 to ncols(A) do
              r:=r+(-1)^(1+j)*A[1,j]*minor(A,1,j)
           end;
        end;
     end;
     return(r)
  end:

• B := Dom::Matrix(Dom::Integer)(
     [[3,2,5,4], [2,5,3,8], [1,2,3,0], [2,3,4,5]]
  ):

• Det(B)

• eval(%)

• eval(%)

• eval(%)

   28