View of /trunk/NationalProblemLibrary/ASU-topics/set119MatrixAlgebra/p14.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 "extraAnswerEvaluators.pl"
   31 ) ;
   32 ############
   33 
   34 TEXT(&beginproblem);
   35 $showPartialCorrectAnswers = 1 ;
   36 
   37 $alpha = non_zero_random(-6,6);
   38 $a = non_zero_random(-6,6);
   39 $gamma = random(-6,6);
   40 
   41 $b11 = random(-3,3);
   42 $b12 = random(-3,3);
   43 $b22 = random(-3,3);
   44 $b21 = ($alpha -1)*($b22+2*$b12)-$alpha*$gamma-2*$b11;
   45 
   46 $c13 = $alpha -1;
   47 $na = -$a;
   48 if ($gamma != 0) {$ngamma = -$gamma;}
   49 else {$ngamma = $gamma;}
   50 
   51 BEGIN_TEXT
   52 Determine the value(s) of  \(x \)  such that
   53 \[
   54 \left[ \begin{array}{ccc}
   55 x & 2 & 1
   56 \end{array}\right]
   57   \left[ \begin{array}{ccc}
   58 $a      & $ngamma  & $na \\
   59 $ngamma & $b11        & $b12  \\
   60 $na & $b21 & $b22
   61 \end{array} \right]
   62  \left[ \begin{array}{c}
   63 x \\
   64 -1 \\
   65 $c13
   66 \end{array}\right] = 0
   67 \]
   68 
   69 $BR
   70 \( x \) = \{ ans_rule(30) \}
   71 $BR
   72 $BBOLD Note: $EBOLD
   73 If there is more than one value write them separated by commas.
   74 $BR
   75 
   76 END_TEXT
   77 
   78 
   79 $x1=$gamma/$a;
   80 $x2=$alpha;
   81 ANS(number_list_cmp("$x1,$x2"));
   82 
   83 
   84 ENDDOCUMENT() ;