## DESCRIPTION
## Matrix Algebra
## ENDDESCRIPTION

## KEYWORDS('Algebra' 'Matrix' 'Matrices' 'True' 'False')
## Tagged by tda2d

## DBsubject('Algebra')
## DBchapter('Linear Algebra')
## DBsection('Matrix Algebra')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl", 
"PGmatrixmacros.pl",
"PGasu.pl",
);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 1;

$m = random(2,5);

do {$n = random(2,9);} until ($n != $m);
do {$r = random(2,9);} until ($r != $m & $r != $n);



BEGIN_TEXT
If A is \( $m \times $n, \)  B is \( $r \times $m \) and C is \( $n \times $r \) then:
$BR
a) BA has dimension $SPACE  \{ans_rule(8)\} \( \times \)  \{ans_rule(8)\}
$BR
b) CB has dimension $SPACE  \{ans_rule(8)\} \( \times \)  \{ans_rule(8)\}
$BR
c) AC has dimension $SPACE  \{ans_rule(8)\} \( \times \)  \{ans_rule(8)\}

END_TEXT

ANS(num_cmp($r));  ANS(num_cmp($n));
ANS(num_cmp($n));  ANS(num_cmp($m));
ANS(num_cmp($m));   ANS(num_cmp($r));

ENDDOCUMENT();       # This should be the last executable line in the problem.