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Sat Jul 24 17:09:50 2010 UTC (2 years, 10 months ago) by ted shifrin
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    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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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