View of /trunk/NationalProblemLibrary/ASU-topics/set119MatrixAlgebra/p10.pg

    1 ## DESCRIPTION
    2 ## Matrix Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Algebra' 'Matrix' 'Matrices')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Linear Algebra')
   10 ## DBsection('Matrix Algebra')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT() ;
   21 
   22 loadMacros(
   23 "PGasu.pl",
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl",
   29 "PGdiffeqmacros.pl",
   30 "PGmatrixmacros.pl"
   31 ) ;
   32 ############
   33 
   34 TEXT(&beginproblem);
   35 
   36 
   37 foreach $i (0..2) {
   38 
   39    foreach $j (0..2) {
   40       $a[$i][$j] = random(-4,4,1);
   41       $b[$i][$j] = random(-4,4,1);
   42     }
   43 }
   44 
   45 
   46 $showPartialCorrectAnswers = 1 ;
   47 
   48 BEGIN_TEXT
   49 
   50 If
   51 \[ A = \left[\begin{array}{ccc}
   52 \{join("& ",@{$a[0]}[0..$#{$a[0]}])\} \cr
   53 \{join("& ",@{$a[1]}[0..$#{$a[1]}])\} \cr
   54 \{join("& ",@{$a[2]}[0..$#{$a[2]}])\} \cr
   55 \end{array}\right]
   56 \mbox{ \ \ and \ \ \ }
   57 B = \left[\begin{array}{ccc}
   58 \{join("& ",@{$b[0]}[0..$#{$b[0]}])\} \cr
   59 \{join("& ",@{$b[1]}[0..$#{$b[1]}])\} \cr
   60 \{join("& ",@{$b[2]}[0..$#{$b[2]}])\} \cr
   61 \end{array}\right],
   62 \]
   63 
   64 then
   65 
   66 $BCENTER
   67 \{ mbox(
   68 '\( 3A-B = \)',
   69 display_matrix([[ans_rule(5),ans_rule(5),ans_rule(5)],
   70 [ans_rule(5),ans_rule(5),ans_rule(5)],
   71 [ans_rule(5),ans_rule(5),ans_rule(5)]],
   72 'align'=>"ccc"))
   73 \}
   74 $ECENTER
   75 END_TEXT
   76 foreach $i (0..2) {
   77 
   78    foreach $j (0..2) {
   79       ANS(num_cmp(3*$a[$i][$j] -$b[$i][$j])  );
   80     }
   81 }
   82 
   83 
   84 
   85 ENDDOCUMENT() ;
   86