View of /trunk/NationalProblemLibrary/ASU-topics/set119MatrixAlgebra/p7.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 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl",
   28 "PGdiffeqmacros.pl",
   29 
   30 ) ;
   31 ############
   32 
   33 TEXT(&beginproblem);
   34 
   35 
   36 foreach $i (0..1) {
   37 
   38    foreach $j (0..2) {
   39       $a[$i][$j] = random(-4,4,1);
   40       $b[$i][$j] = random(-4,4,1);
   41     }
   42 }
   43 
   44 foreach $i (0..1) {
   45 
   46    foreach $j (0..2) {
   47       $c[$i][$j] = $a[$i][$j]+$b[$i][$j];
   48 
   49     }
   50 }
   51 
   52 $showPartialCorrectAnswers = 1 ;
   53 
   54 BEGIN_TEXT
   55 Determine \(x \) and \( y\) such that
   56 
   57 \[
   58 \left[\begin{array}{ccc}
   59 \{join("& ",@{$a[0]}[0..$#{$a[0]}])\} \cr
   60 \{join("& ",@{$a[1]}[0..$#{$a[1]}])\}
   61 \end{array}\right]
   62  + \left[\begin{array}{ccc}
   63 x-y      & $b[0][1] & $b[0][2] \\
   64 $b[1][0] & x        & $b[1][2]
   65 \end{array} \right]
   66 = \left[\begin{array}{ccc}
   67 $c[0][0] & $c[0][1] & $c[0][2] \\
   68 $c[1][0] & 2 x +y   & $c[1][2]
   69 \end{array}\right]
   70 \]
   71 
   72 $BR
   73 \( x = \) $SPACE  \{ ans_rule(10) \}
   74 $BR
   75 \( y = \) $SPACE \{ans_rule(10) \}
   76 
   77 
   78 END_TEXT
   79 
   80 
   81 $x=($b[0][0]+$a[1][1])/2;
   82 $y=($a[1][1]-$b[0][0])/2;
   83 ANS(num_cmp($x));
   84 ANS(num_cmp($y));
   85 
   86 ENDDOCUMENT() ;