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Wed Feb 22 20:38:15 2006 UTC (7 years, 2 months ago) by jjholt
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--JH


    1 ## DESCRIPTION
2 ## Systems of Linear Equations
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Algebra' 'Linear Equations' 'Matrix' 'Matrices')
6 ## Tagged by tda2d
7
8 ## DBsubject('Algebra')
9 ## DBchapter('Systems of Equations and Inequalities')
10 ## DBsection('Systems of Linear Equations')
11 ## Date('')
12 ## Author('')
13 ## Institution('ASU')
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 "PGasu.pl",
24 "PG.pl",
25 "PGbasicmacros.pl",
26 "PGchoicemacros.pl",
28 "PGgraphmacros.pl",
29 "PGauxiliaryFunctions.pl",
31
32 );
33
34 TEXT(&beginproblem);
35 $showPartialCorrectAnswers = 0; 36 install_problem_grader(~~&std_problem_grader); 37 38$a11=non_zero_random(-6,6,2);
39 $a12=non_zero_random(-5,5,1); 40$a13=random(-5,5,2);
41 $a21=random(-5,5,2); 42$a22=non_zero_random(-6,6,2);
43 $a23=non_zero_random(-6,6,2); 44$a31=non_zero_random(-6,6,1);
45 $a32=random(-5,5,2); 46$d = $a21*$a32-$a22*$a31;
47 do {$a33=non_zero_random(-6,6,2);} until 48 ($a11*($a22*$a33-$a23*$a32)-$a12*($a21*$a33-$a23*$a31)+$a13*$d != 0); 49 50$x=random(-5,5,1);
51 $y=random(-5,5,1); 52$z=random(-5,5,1);
53
54 $b1 =$a11*$x +$a12*$y +$a13*$z; 55$b2 = $a21*$x + $a22*$y + $a23*$z;
56 $b3 =$a31*$x +$a32*$y +$a33*$z; 57 58$NO_SPACE = '@{}';
59
60 $ls1 = nicestring([$a11,$a12,$a13],['x','y','z']);
61 $ls2 = nicestring([$a21,$a22,$a23],['x','y','z']);
62 $ls3 = nicestring([$a31,$a32,$a33],['x','y','z']);
63
64 $mc = new_multiple_choice(); 65$mc->qa("How many solutions are there to this system?",
66 "Exactly 1");
67 $mc->makeLast("None", 68 "Exactly 1", 69 "Exactly 2", 70 "Exactly 3", 71 "Infinitely many", 72 "None of the above"); 73 74 BEGIN_TEXT 75$PAR
76 Solve the system using matrices (row operations) $BR 77 $\left\{ "\{"; \} 78 \begin{array}{r{NO_SPACE}r{NO_SPACE}} 79 ls1 &= b1 \cr 80 ls2 &= b2 \cr 81 ls3&= b3 82 \end{array}\right.$ 83 84 \{$mc->print_q() \}
85         $PAR 86 \{$mc->print_a() \}
87 $BR 88 END_TEXT 89 ANS(radio_cmp($mc->correct_ans));
90
91 $ans1 =$inputs_ref->{AnSwEr1};
92 if(defined($ans1)) { 93 if($ans1 eq "D") {
94 TEXT("${BBOLD}Note:$EBOLD
95 each solution to this system is an ordered triplet with three coordinates.  Together,
96 the three coordinates make one solution.  Having exactly three solutions is
97 not possible.");
98  } elsif($ans1 eq "C") { 99 TEXT("${BBOLD}Note:$EBOLD 100 it is not possible for a linear system of equations to ever have exactly 2 solutions."); 101 }} 102 103 104 BEGIN_TEXT 105 106$HR
107
108 $BR 109 If there is one solution, give its coordinates in the answer spaces below. 110$PAR
111 If there
112 are infinitely many solutions, enter ${BITALIC}z$EITALIC in the answer blank for $$z$$,
113 enter a formula for $$y$$ in terms of $$z$$ in the answer blank for $$y$$ and
114 enter a formula for $$x$$ in terms of $$z$$ in the answer blank for $$x$$.
115 $PAR 116 If there are no solutions, leave the answer blanks for $$x$$, $$y$$ and $$z$$ empty. 117$BR$BR 118 $$x =$$ \{ans_rule(40) \} 119$BR$BR 120 $$y =$$ \{ans_rule(40) \} 121$BR$BR 122 $$z =$$ \{ans_rule(40) \} 123 124 END_TEXT 125 126 # we use fun_cmp so it doesn't give a syntax error if they try functions 127 # it still works since we are comparing to a "constant" function, which 128 # is the same as comparing to a number 129 130 ANS(fun_cmp("$x",vars=>["z"]));
131 ANS(fun_cmp("$y",vars=>["z"])); 132 ANS(fun_cmp("$z",vars=>["z"]));
133
134 # If there were no solutions, we would use
135 # ANS(auto_right("this answer can be left blank"));
136 # ANS(auto_right("this answer can be left blank"));
137
138 ENDDOCUMENT();        # This should be the last executable line in the problem.
139