## DESCRIPTION
## Matrix Algebra
## ENDDESCRIPTION
## Tagged by tda2d
## DBsubject(Linear algebra)
## DBchapter(Matrices)
## DBsection(Matrix algebra)
## Institution(ASU)
## MLT(matrix_mult)
## Level(2)
## KEYWORDS('Algebra' 'Matrix' 'Matrices')
DOCUMENT() ;
loadMacros(
"PGstandard.pl",
"PGasu.pl",
"PGchoicemacros.pl",
"PGdiffeqmacros.pl",
"PGmatrixmacros.pl",
"PGcourse.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
\[ A = \left[\begin{array}{ccc}
\{join("& ",@{$a[0]}[0..$#{$a[0]}])\} \cr
\{join("& ",@{$a[1]}[0..$#{$a[1]}])\} \cr
\{join("& ",@{$a[2]}[0..$#{$a[2]}])\} \cr
\end{array}\right]
\quad \mbox{ and } \quad
B = \left[\begin{array}{ccc}
\{join("& ",@{$b[0]}[0..$#{$b[0]}])\} \cr
\{join("& ",@{$b[1]}[0..$#{$b[1]}])\} \cr
\{join("& ",@{$b[2]}[0..$#{$b[2]}])\} \cr
\end{array}\right]
\]
then
$BCENTER
\{ mbox(
'\( A B = \)',
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
and
$BCENTER
\{ mbox(
'\( BA = \)',
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) {
$sum = 0;
foreach $k (0..2) {
$sum = $sum + $a[$i][$k]*$b[$k][$j];
}
ANS(num_cmp($sum) );
}
}
foreach $i (0..2) {
foreach $j (0..2) {
$sum = 0;
foreach $k (0..2) {
$sum = $sum + $b[$i][$k]*$a[$k][$j];
}
ANS(num_cmp($sum) );
}
}
ENDDOCUMENT() ;