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| 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 : |
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