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

 1 : jjholt 200 ## DESCRIPTION 2 : ## Linear Algebra 3 : ## ENDDESCRIPTION 4 : jj 144 5 : jjholt 200 ## KEYWORDS ('linear algebra','vector space','linear transformation') 6 : ## Tagged by cmd6a 5/3/06 7 : jj 144 8 : jjholt 200 ## DBsubject('Linear Algebra') 9 : ## DBchapter('Vector Spaces') 10 : ## DBsection('Linear Transformations') 11 : ## Date('') 12 : ## Author('') 13 : ## Institution('Rochester') 14 : ## TitleText1('') 15 : ## EditionText1('') 16 : ## AuthorText1('') 17 : ## Section1('') 18 : ## Problem1('') 19 : 20 : 21 : jj 144 DOCUMENT(); # This should be the first executable line in the problem. 22 : 23 : loadMacros( 24 : "PG.pl", 25 : "PGbasicmacros.pl", 26 : "PGchoicemacros.pl", 27 : "PGanswermacros.pl", 28 : "PGgraphmacros.pl", 29 : "PGmatrixmacros.pl", 30 : "PGnumericalmacros.pl", 31 : "PGauxiliaryFunctions.pl" 32 : ); 33 : 34 : TEXT(beginproblem()); 35 : $showPartialCorrectAnswers = 0; 36 : 37 : @coeff = (2, 3, 4, 5, 6, 7, 8, 9, 10); 38 : @slice = NchooseK(9,9); 39 : @c = @coeff[@slice]; 40 : 41 :$NO_SPACE = '@{}'; 42 : 43 : @linear = ('$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 44 : y_1 & = & c[0] x_1 + x_2 \cr 45 : y_2 & = & - x_1 46 : \end{array} \right .$$', 47 : '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 48 : y_1 & = & 0 \cr 49 : y_2 & = & c[1] x_2 50 : \end{array} \right .$$', 51 : '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 52 : y_1 & = & c[2] x_2 \cr 53 : y_2 & = & - c[3] x_3 \cr 54 : y_3 & = & - c[4] x_1 55 : \end{array} \right .$$', 56 : '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 57 : y_1 & = & c[5] x_1 - c[6] x_2 + c[7] x_3 \cr 58 : y_2 & = & c[8] x_2 - c[0] x_3 \cr 59 : y_3 & = & - c[2] x_1 - c[1] x_2 60 : \end{array} \right .$$', 61 : '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 62 : y_1 & = & - c[7] x_1 \cr 63 : y_2 & = & c[6] x_1 \cr 64 : y_3 & = & c[3] x_1 65 : \end{array} \right .$$'); 66 : 67 : @nonlin = ('$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 68 : y_1 & = & c[4] x_1 \cr 69 : y_2 & = & c[5] \cr 70 : \end{array} \right .$$', 71 : '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 72 : y_1 & = & 0 \cr 73 : y_2 & = & x_1 x_2 \cr 74 : \end{array} \right .$$', 75 : '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 76 : y_1 & = & x_1 + c[8] \cr 77 : y_2 & = & x_2 78 : \end{array} \right .$$', 79 : '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 80 : y_1 & = & c[0] \cr 81 : y_2 & = & c[1] \cr 82 : y_3 & = & c[2] \cr 83 : \end{array} \right .$$', 84 : '$$\left\{ \begin{array}{r{NO_SPACE}r{NO_SPACE}l} 85 : y_1 & = & x_2^2 \cr 86 : y_2 & = & x_3 \cr 87 : y_3 & = & x_1 \cr 88 : \end{array} \right .$$'); 89 : 90 : @slice1 = NchooseK(5,3); 91 : @slinear = @linear[@slice1]; 92 : 93 : @slice2 = NchooseK(5,3); 94 : @snonlin = @nonlin[@slice2]; 95 : 96 : $cmc = new_checkbox_multiple_choice(); 97 :$cmc -> qa ("Which of the following transformations are linear?", 98 : $slinear[0],$slinear[1], $slinear[2]); 99 :$cmc -> extra ($snonlin[0],$snonlin[1], $snonlin[2]); 100 : 101 : BEGIN_TEXT 102 : 103 :$BR 104 : \{$cmc -> print_q \} 105 :$BR 106 : \{$cmc -> print_a \} 107 : 108 : END_TEXT 109 : 110 : ANS(checkbox_cmp($cmc->correct_ans )); 111 : 112 : ENDDOCUMENT(); # This should be the last executable line in the problem. 113 :