## DESCRIPTION
## Matrix Algebra
## ENDDESCRIPTION

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

## DBsubject('Algebra')
## DBchapter('Systems of Equations and Inequalities')
## DBsection('The Algebra of Matrices')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT() ;        

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

TEXT(beginproblem());


foreach $i (0..2) {

   foreach $j (0..2) {
   		$a[$i][$j] = random(-4,4,1);
   		$b[$i][$j] = random(-4,4,1);
   	}
}


$showPartialCorrectAnswers = 1 ;

BEGIN_TEXT

If 
\[ A = \left[\begin{array}{ccc}
\{join("& ",@{$a[0]}[0..$#{$a[0]}])\} \cr
\{join("& ",@{$a[1]}[0..$#{$a[1]}])\} \cr
\{join("& ",@{$a[2]}[0..$#{$a[2]}])\} \cr
\end{array}\right]
\mbox{ \ \ and \ \ \ }
B = \left[\begin{array}{ccc}
\{join("& ",@{$b[0]}[0..$#{$b[0]}])\} \cr
\{join("& ",@{$b[1]}[0..$#{$b[1]}])\} \cr
\{join("& ",@{$b[2]}[0..$#{$b[2]}])\} \cr
\end{array}\right],
\]

then

$BCENTER
\{ mbox(
'\( 3A-B = \)',
display_matrix([[ans_rule(5),ans_rule(5),ans_rule(5)],
[ans_rule(5),ans_rule(5),ans_rule(5)],
[ans_rule(5),ans_rule(5),ans_rule(5)]],
'align'=>"ccc"))
\}
$ECENTER
END_TEXT
foreach $i (0..2) {

   foreach $j (0..2) {
   		ANS(num_cmp(3*$a[$i][$j] -$b[$i][$j])  );
   	}
}



ENDDOCUMENT() ;