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

 1 : jj 144 ##DESCRIPTION 2 : ##KEYWORDS(linear, transformation) 3 : ## 4 : ##ENDDESCRIPTION 5 : 6 : 7 : DOCUMENT(); # This should be the first executable line in the problem. 8 : 9 : loadMacros( 10 : "PG.pl", 11 : "PGbasicmacros.pl", 12 : "PGchoicemacros.pl", 13 : "PGanswermacros.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 :