## DESCRIPTION
## Answer is a matrix
## ENDDESCRIPTION

## DBsubject(WeBWorK)
## DBchapter(WeBWorK tutorial)
## DBsection(PGML tutorial 2015)
## Date(06/01/2015)
## Institution(Hope College)
## Author(Paul Pearson)
## MO(1)
## KEYWORDS('matrix')


##################
#   Initialization 
DOCUMENT();

loadMacros(
  "PGstandard.pl",
  "PGML.pl",
  "MathObjects.pl",
  "AnswerFormatHelp.pl",
  "parserMultiAnswer.pl",
  "scaffold.pl",
  "PGcourse.pl",
);

TEXT(beginproblem());

$showPartialCorrectAnswers = 1;

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

Context("Matrix");

$A = Matrix([
[random(-5,5,1),random(-5,5,1),random(-5,5,1)],
[random(-5,5,1),random(-5,5,1),random(-5,5,1)],
]);

$B = Matrix([
[random(-5,5,1),random(-5,5,1),random(-5,5,1)],
[random(-5,5,1),random(-5,5,1),random(-5,5,1)],
]);


###########################################
#  The scaffold
Scaffold::Begin(can_open => "when_previous_correct", is_open => "correct_or_first_incorrect");

###########################################
Section::Begin("Part 1: Identify correct dimension");

$nrows_ans = 2;
$ncols_ans = 2;
BEGIN_PGML
Suppose
>> [``A = [$A] \ \ \mbox{and} \ \ B = [$B]. ``] <<
Evaluate the following matrix product.

Detemine [`n`] and [`m`] such that [` A B^T \in M_{n\times m}`]

[`n= `][__]{$nrows_ans}
[`m= `][__]{$ncols_ans} [@ AnswerFormatHelp("numbers") @]*
END_PGML

BEGIN_PGML_SOLUTION
Solution goes here.
END_PGML_SOLUTION

Section::End();

###########################################
Section::Begin("Part 2: Evaluate the product");

$answer = $A * ($B->transpose);
BEGIN_PGML
[` A B^T = `][_____]*{$answer} [@ AnswerFormatHelp("matrices") @]*
END_PGML

BEGIN_PGML_SOLUTION
Solution goes here.
END_PGML_SOLUTION

Section::End();
###########################################

Scaffold::End();
ENDDOCUMENT();