** Using WeBWorK **

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

DOCUMENT();

loadMacros(
   "PGstandard.pl",     # Standard macros for PG language
   "MathObjects.pl",
   #"source.pl",        # allows code to be displayed on certain sites.
   #"PGcourse.pl",      # Customization file for the course
);

# Print problem number and point value (weight) for the problem
TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect
$showPartialCorrectAnswers = 1;

##############################################################
#
#  Setup
#
#
Context("Matrix");
Context()->variables->add(a=>'Real',b=>'Real');
$a = Matrix("[[1,1],[0,1]]");
$b = Matrix("[[1,0],[1,1]]");
$f = Matrix("$a $b");

##############################################################
#
#  Text
#
#

Context()->texStrings;
BEGIN_TEXT
Please enter 'a b' (without quotes): \{ ans_rule(10) \}
END_TEXT
Context()->normalStrings;

##############################################################
#
#  Answers
#
#

$checker = sub {
 my $in = shift @_;
  my $correctQ=0;
  my $student_matrix;
 my $student_value = $in;
if ($in) {
 $student_value=~ s/a/~~$a/;
 $student_value=~ s/b/~~$b/;
 $student_matrix = PG_restricted_eval($student_value);
 $correctQ = ($student_matrix == $f );
}
    my $rh_answer = new AnswerHash(
             score  => $correctQ,
	     correct_ans  	=> 	"a*b",
	     student_ans  	=> 	$in,
	     ans_message   	=> 	$student_matrix,
	     type		   	=> 	'custom'
    );
    $rh_answer;

};
ANS($checker);



ENDDOCUMENT();        

This will accept   a*b  as a correct answer.  It mark b*a incorrect.

It will give mysterious perl like errors if you enter ab or ba.

Still it's a start -- and shows that this kind of answer checking is possible. 

  Context("Numeric");
  Context()->constants->add(
    a => Matrix([1,2],[3,4]),
    b => Matrix([pi,e],[0,sqrt(2)]),
  );

There is still a possibility that two different expressions in a and b that have the same value (since they are specific matrices, not variables), but I think it would be hard to come up with an example.

Note that there are a lot of operations you can't perform on a and b, like division, square roots, trig functions, etc., so you might want to remove those from the context.

Davide