View of /branches/UGA/4.1.1.pg

    1 ## DESCRIPTION
    2 ## Linear Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('linear algebra','linear system')
    6 ## Tagged by cmd6a 5/3/06
    7 
    8 ## DBsubject('Linear Algebra')
    9 ## DBchapter('Systems of Linear Equations and Matrices')
   10 ## DBsection('Introduction to Systems of Linear Equations')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   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 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGgraphmacros.pl",
   28 "PGmatrixmacros.pl",
   29 "PGnumericalmacros.pl",
   30 "PGauxiliaryFunctions.pl",
   31 # "PGmorematrixmacros.pl"
   32 );
   33 
   34 TEXT(beginproblem());
   35 $showPartialCorrectAnswers = 1;
   36 
   37 $a = random(4,5,1);
   38 $apb = random(-1,1,2);
   39 $b = $apb - $a;
   40 $c = random(2,4,1);
   41 $d = random(2,4,1);
   42 $e = random(0,4,1);
   43 
   44 $f = random(2,3,1);
   45 $g = random(2,3,1);
   46 $h = random(1,5,1);
   47 
   48 $i = $a - 1;
   49 $j = $b + 1;
   50 $k = $c + $f;
   51 $l = $d + $g;
   52 $m = $e + $h;
   53 
   54 $p = random(2,3,1) * random(-1,1,2);
   55 $n = - $p;
   56 $q = $p * $f;
   57 $r = $p * $g;
   58 $s = $p * $h;
   59 
   60 $NO_SPACE = '@{}';
   61 
   62 BEGIN_TEXT
   63 
   64 Give the general solution of the system
   65 \[ \left\{'\{'\} \begin{array}{r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r}
   66 $a x_1 & + $b x_2 & + $c x_3 & + $d x_4 = & $e \cr
   67  - x_1 &    + x_2 & + $f x_3 & + $g x_4 = & $h \cr
   68 $i x_1 & + $j x_2 & + $k x_3 & + $l x_4 = & $m \cr
   69 $n x_1 & + $p x_2 & + $q x_3 & + $r x_4 = & $s
   70 \end{array} \right. \]
   71 in standard form.
   72 $BR
   73 \{ mbox( display_matrix([['\(x_1\)'], ['\(x_2\)'], ['\(x_3\)'], ['\(x_4\)']]), '\(=\)', answer_matrix(4,1,5), '\( + \quad s\)', answer_matrix(4,1,5),
   74 '\( + \quad t\)', answer_matrix(4,1,5),  ',' ) \}
   75 $BR
   76 where \(s\) is the free variable \(x\)_\{ans_rule(1)\} and \(t\) is the free variable \(x\)_\{ans_rule(1)\}, arranged in increasing order. (Sorry, no subscripts for answers in WeBWork!)
   77 
   78 END_TEXT
   79 
   80 $t = $apb*($a*$f+$c) - $f;
   81 $u = $apb*($a*$g+$d) - $g;
   82 $v = $apb*($a*$h+$e) - $h;
   83 
   84 $w = $apb*($a*$f+$c);
   85 $x = $apb*($a*$g+$d);
   86 $y = $apb*($a*$h+$e);
   87 
   88 # ans_array(4,1,5), '\(+ \quad s\)', ans_array_extension(4,1,5),  '\(+ \quad
   89 # t\)', ans_array_extension(4,1,5),
   90 
   91 # ANS(vec_solution_cmp([[$v,$y,0,0], [-$t,-$w,1,0], [-$u,-$x,0,1]]));
   92 ANS(num_cmp($v)); ANS(num_cmp($y)); ANS(num_cmp(0)); ANS(num_cmp(0));
   93 ANS(num_cmp(-$t)); ANS(num_cmp(-$w)); ANS(num_cmp(1)); ANS(num_cmp(0));
   94 ANS(num_cmp(-$u)); ANS(num_cmp(-$x)); ANS(num_cmp(0)); ANS(num_cmp(1));
   95 ANS(num_cmp(3));
   96 ANS(num_cmp(4));
   97 
   98 
   99 ENDDOCUMENT();       # This should be the last executable line in the problem.
  100