** Using WeBWorK **

## 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) {</div> <div><br /></div> <div> foreach $j (0..2) {</div> <div> <span style="white-space:pre;"> </span>$a[$i][$j] = random(-4,4,1);</div> <div> <span style="white-space:pre;"> </span>$b[$i][$j] = random(-4,4,1);</div> <div> <span style="white-space:pre;"> </span>}

}

$showPartialCorrectAnswers = 1 ;

BEGIN_TEXT

If

\{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(</div> <div>'\( A B = \)',</div> <div>display_matrix([[ans_rule(5),ans_rule(5),ans_rule(5)],</div> <div>[ans_rule(5),ans_rule(5),ans_rule(5)],</div> <div>[ans_rule(5),ans_rule(5),ans_rule(5)]],</div> <div>'align'=>"ccc")),</div> <div>\}

$ECENTER

and

$BCENTER

\{ mbox(</div> <div>'\( BA = \)',</div> <div>display_matrix([[ans_rule(5),ans_rule(5),ans_rule(5)],</div> <div>[ans_rule(5),ans_rule(5),ans_rule(5)],</div> <div>[ans_rule(5),ans_rule(5),ans_rule(5)]],</div> <div>'align'=>"ccc")),</div> <div>\}

$ECENTER

END_TEXT

foreach $i (0..2) {</div> <div><br /></div> <div> foreach $j (0..2) {</div> <div> $sum = 0;</div> <div> foreach $k (0..2) {</div> <div> $sum = $sum + $a[$i][$k]*$b[$k][$j];</div> <div> }

 ANS(num_cmp($sum) );

}

}

foreach $i (0..2) {</div> <div><br /></div> <div> foreach $j (0..2) {</div> <div> $sum = 0;</div> <div> foreach $k (0..2) {</div> <div> $sum = $sum + $b[$i][$k]*$a[$k][$j];</div> <div> }

 ANS(num_cmp($sum) );

}

}

ENDDOCUMENT() ;