View of /trunk/NationalProblemLibrary/ASU-topics/set119MatrixAlgebra/p8.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();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGasu.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl",
   29 "PGgraphmacros.pl",
   30 "PGmatrixmacros.pl"
   31 );
   32 
   33 TEXT(beginproblem());
   34 $showPartialCorrectAnswers = 1;
   35 
   36 $NO_SPACE = '@{}';
   37 
   38 $a11 = non_zero_random(-10,10,1);
   39 $a12 = non_zero_random(-10,10,1);
   40 $a21 = non_zero_random(-10,10,1);
   41 $a22 = random(-10,10,1);
   42 
   43 $b11 = random(-10,10,1);
   44 $b12 = non_zero_random(-10,10,1);
   45 $b21 = non_zero_random(-10,10,1);
   46 $b22 = non_zero_random(-10,10,1);
   47 
   48 $mult = random(2,5,1);
   49 
   50 $ans11 = $mult*($a11 * $b11 + $a12 * $b21) ;
   51 $ans12 =$mult*( $a11 * $b12 + $a12 * $b22) ;
   52 $ans21 = $mult*($a21 * $b11 + $a22 * $b21) ;
   53 $ans22 = $mult*($a21 * $b12 + $a22 * $b22) ;
   54 
   55 
   56 
   57 BEGIN_TEXT
   58 
   59 If
   60 \[ A = \left[ \begin{array}{cc}
   61 \{join("& ",$a11,$a12 ) \}\cr
   62 \{join("& ",$a21,$a22 ) \}\cr
   63 \end{array} \right] \mbox{ \ and \ \ }
   64 B = \left[ \begin{array}{cc}
   65 \{join("& ",$b11,$b12 ) \}\cr
   66 \{join("& ",$b21,$b22 ) \}\cr
   67 \end{array} \right], \]
   68 
   69 then
   70 
   71 $BCENTER
   72 \{ mbox(
   73 '\( A($mult B) = \)',
   74 display_matrix([[ans_rule(5),ans_rule(5)]
   75 ,[ans_rule(5),ans_rule(5)]],
   76 'align'=>"cc"))
   77 \}
   78 $ECENTER
   79 END_TEXT
   80 
   81 ANS(num_cmp($ans11));
   82 ANS(num_cmp($ans12));
   83 ANS(num_cmp($ans21));
   84 ANS(num_cmp($ans22));
   85 
   86 
   87 
   88 ENDDOCUMENT();       # This should be the last executable line in the problem.