DOCUMENT();


loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  # Used to provide contextual help for how to type answers.
  "AnswerFormatHelp.pl",
  # Provides greater control over the layout of the problem.
  "PGML.pl",
  # Used for course-specific initializations.
  "PGcourse.pl",
);

TEXT(beginproblem());

#############################
#  Setup

# Used for handling matrix problems.
Context("Matrix");

#-ULETH-#
# ans : the random value of the determinant for the question.
# M : A solution matrix used to verify a student answer or act as a solution set.

$ans = non_zero_random(-10,10,1);

$M = Matrix([
  [$ans,6,1,9],
  [0,1,3,4],
  [0,0,1,6],
  [0,0,0,1],
]);

#-ENDULETH-#

#############################

#  Main text
#-ULETH-#

BEGIN_PGML
###Enter a non-diagonal 4x4 matrix with a determinant of [$ans].

[`A =`] [@ $M->ans_array(5) @]* [@ AnswerFormatHelp("matrices") @]*
END_PGML

#-ENDULETH-#

#-ULETH-#

$showPartialCorrectAnswers = 0;
ANS( $M->cmp(
     checker => sub {
       my ($M,$student,$ansHash) = @_; 
       my ($sdet)=$student->det();
       if ( $sdet != $ans ) {
         $ansHash->{ans_message} = "The determinant of your matrix is not so does not satisfy the conditions." unless $ansHash->{isPreview};
         return 0;
       }
       # Check if diagonal
       my $isDiag = 1;
       my $zz = Real(0);
       for ( my $ii = 1; $ii <= 3 ; $ii++ ) {
         for ( my $jj = 1 + $ii; $jj <= 3 ; $jj++ ) {
           if ( ( $student->element($ii,$jj) != $zz ) || ( $student->element($jj,$ii) != $zz ) ) {
             $isDiag = 0;
             last;
           }
          last if ( $isDiag == 0 );
         }
       }
       if ( $isDiag == 1 ) {
         $ansHash->{ans_message} = "Your matrix is a diagonal matrix so does not satisfy the conditions." unless $ansHash->{isPreview};
         return 0;
       } else {
         return 1;
       }
       # should not get here
       $ansHash->{ans_message} = "Error in the grading code. Please report this." unless $ansHash->{isPreview};
       return 0;
       }
));

#-ENDULETH-#

#############################

#  Solution
#-ULETH-#

BEGIN_PGML_SOLUTION
SOLUTION:

One possible solution is [`A = [$M]`].

We know that the determinant of any upper triangular matrix is the product of the element along the diagonal. So by placing [`[$ans]`] anywhere on the diagonal and filling the upper half of the matrix with any numbers (since they do not effect the determinant).

END_PGML_SOLUTION

COMMENT('
    Randomization provides 19 different possible versions of this question.<BR>
    Includes a solution set.<BR>
    Recommended Settings:<BR>
    - Weight: 2<BR>
    - Max attempts: Unlimited<BR>
    - Show me another: -2<BR>
    - Rerandomize after: Default<BR>
    Made from a ULETH template.<BR>
    ');
#-ENDULETH-#

ENDDOCUMENT();