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# View of /branches/UGA/4.1.7.pg

Sat Jul 24 17:09:50 2010 UTC (2 years, 9 months ago) by ted shifrin
File size: 2249 byte(s)
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    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
23            "PGbasicmacros.pl",
24            "PGchoicemacros.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.