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# View of /trunk/NationalProblemLibrary/Rochester/setLinearAlgebra14TransfOfRn/ur_la_14_9.pg

Sun Mar 26 15:53:04 2006 UTC (7 years, 1 month ago) by jj
File size: 3129 byte(s)
Initial import


    1 ##DESCRIPTION
2 ##KEYWORDS(linear, transformation)
3 ##
4 ##ENDDESCRIPTION
5
6
7 DOCUMENT();        # This should be the first executable line in the problem.
8
10 "PG.pl",
11 "PGbasicmacros.pl",
12 "PGchoicemacros.pl",
14 "PGgraphmacros.pl",
15 "PGmatrixmacros.pl",
16 "PGnumericalmacros.pl",
17 "PGauxiliaryFunctions.pl"
18 );
19
20 TEXT(beginproblem());
21 $showPartialCorrectAnswers = 0; 22 23 @coeff = (2, 3, 4, 5, 6, 7, 8, 9, 10); 24 @slice = NchooseK(9,9); 25 @c = @coeff[@slice]; 26 27$NO_SPACE = '@{}';
28
29 @linear = ('$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 30 y_1 & = & c[0] x_1 + x_2 \cr 31 y_2 & = & - x_1 32 \end{array} \right .$$',
33             '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 34 y_1 & = & 0 \cr 35 y_2 & = & c[1] x_2 36 \end{array} \right .$$',
37             '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 38 y_1 & = & c[2] x_2 \cr 39 y_2 & = & - c[3] x_3 \cr 40 y_3 & = & - c[4] x_1 41 \end{array} \right .$$',
42             '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 43 y_1 & = & c[5] x_1 - c[6] x_2 + c[7] x_3 \cr 44 y_2 & = & c[8] x_2 - c[0] x_3 \cr 45 y_3 & = & - c[2] x_1 - c[1] x_2 46 \end{array} \right .$$',
47              '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 48 y_1 & = & - c[7] x_1 \cr 49 y_2 & = & c[6] x_1 \cr 50 y_3 & = & c[3] x_1 51 \end{array} \right .$$');
52
53 @nonlin = ('$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 54 y_1 & = & c[4] x_1 \cr 55 y_2 & = & c[5] \cr 56 \end{array} \right .$$',
57            '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 58 y_1 & = & 0 \cr 59 y_2 & = & x_1 x_2 \cr 60 \end{array} \right .$$',
61            '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 62 y_1 & = & x_1 + c[8] \cr 63 y_2 & = & x_2 64 \end{array} \right .$$',
65            '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 66 y_1 & = & c[0] \cr 67 y_2 & = & c[1] \cr 68 y_3 & = & c[2] \cr 69 \end{array} \right .$$',
70            '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 71 y_1 & = & x_2^2 \cr 72 y_2 & = & x_3 \cr 73 y_3 & = & x_1 \cr 74 \end{array} \right .$$');
75
76 @slice1 = NchooseK(5,3);
77 @slinear = @linear[@slice1];
78
79 @slice2 = NchooseK(5,3);
80 @snonlin = @nonlin[@slice2];
81
82 $cmc = new_checkbox_multiple_choice(); 83$cmc -> qa ("Which of the following transformations are linear?",
84       $slinear[0],$slinear[1], $slinear[2]); 85$cmc -> extra ($snonlin[0],$snonlin[1], $snonlin[2]); 86 87 BEGIN_TEXT 88 89$BR
90 \{$cmc -> print_q \} 91$BR
92 \{$cmc -> print_a \} 93 94 END_TEXT 95 96 ANS(checkbox_cmp($cmc->correct_ans ));
97
98 ENDDOCUMENT();       # This should be the last executable line in the problem.
99