View of /branches/UGA/4.1.7.pg

    1 ## DESCRIPTION
    2 ##   Constraint equation for consistency
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Linear equations')
    6 ##
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('')
   10 ## DBsection('')
   11 ## Date('10/04/2009')
   12 ## Author('Ted Shifrin')
   13 ## Institution('UGA')
   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("PGstandard.pl",
   23            "PGbasicmacros.pl",
   24            "PGchoicemacros.pl",
   25            "PGanswermacros.pl",
   26            "PGauxiliaryFunctions.pl",
   27            "PGmatrixmacros.pl",
   28            "PGmorematrixmacros.pl",
   29           );
   30 
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 
   35 $a = non_zero_random(-2, 2, 1);
   36 $b = non_zero_random(-2, 2, 1);
   37 $b1 = non_zero_random(-2, 2, 1);
   38 $c = non_zero_random(-2, 2, 1);
   39 $d = non_zero_random(-2, 2, 1);
   40 $d1 = non_zero_random(-2, 2, 1);
   41 $e = non_zero_random(-3, 3, 1);
   42 $f = non_zero_random(-3, 3, 1);
   43 $i = non_zero_random(-1, 1, 2);
   44 $g = $e*$f+$i;
   45 $k = non_zero_random(-3, 3, 1);
   46 $l = non_zero_random(-3, 3, 1);
   47 $m = non_zero_random(-3, 3, 1);
   48 $n = non_zero_random(-3, 3, 1);
   49 
   50 
   51 $m11=1; $m12=$e; $m13=$a+$e*$c; $m14=$b+$e*$d; $m15=$b1+$e*$d1;
   52 $m21=$f; $m22=$g; $m23=$f*$a+$g*$c; $m24=$f*$b+$g*$d; $m25=$f*$b1+$g*$d1;
   53 $m31=$k; $m32=$l; $m33=$k*$a+$l*$c; $m34=$k*$b+$l*$d; $m35=$k*$b1+$l*$d1;
   54 $m41=$m; $m42=$n; $m43=$m*$a+$n*$c; $m44=$m*$b+$n*$d; $m45=$m*$b1+$n*$d1;
   55 
   56 $ans11=-$k+$i*$f*($l-$e*$k);
   57 $ans12=-$i*($l-$e*$k);
   58 $ans13=1;
   59 $ans14=0;
   60 
   61 $ans21=-$m+$i*$f*($n-$e*$m);
   62 $ans22=-$i*($n-$e*$m);
   63 $ans23=0;
   64 $ans24=1;
   65 
   66 BEGIN_TEXT
   67 
   68 Find the constraint equations for \(A\mathbf x = \mathbf b\) to be consistent, with
   69 
   70 \[ A = \left[\begin{array}{r r r r r}
   71 $m11 & $m12 & $m13 & $m14 & $m15 \cr
   72 $m31 & $m32 & $m33 & $m34 & $m35 \cr
   73 $m21 & $m22 & $m23 & $m24 & $m25 \cr
   74 $m41 & $m42 & $m43 & $m44 & $m45
   75 \end{array} \right]\quad .
   76 \]
   77 
   78 $PAR
   79 
   80 Constraint equations are
   81 
   82 \{ mbox( ans_array(4,1,8), '\(\cdot \ \mathbf b = \quad\)',   ans_array_extension(4,1,8), '\(\cdot \ \mathbf b = 0\ .\)') \}
   83 
   84 
   85 END_TEXT
   86 
   87 ANS(basis_cmp([[$ans11,$ans13,$ans12,$ans14],[$ans21,$ans23,$ans22,$ans24]]));
   88 
   89 
   90 
   91 ENDDOCUMENT();  # This should be the last executable line in the problem.