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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 : | |||
| 8 : | ## 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 : | jj | 144 | DOCUMENT(); # This should be the first executable line in the problem. |
| 21 : | |||
| 22 : | loadMacros( | ||
| 23 : | "PG.pl", | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGchoicemacros.pl", | ||
| 26 : | "PGanswermacros.pl", | ||
| 27 : | "PGgraphmacros.pl", | ||
| 28 : | "PGnumericalmacros.pl", | ||
| 29 : | "PGstatisticsmacros.pl", | ||
| 30 : | "PGmatrixmacros.pl" | ||
| 31 : | ); | ||
| 32 : | |||
| 33 : | TEXT(beginproblem()); | ||
| 34 : | $showPartialCorrectAnswers = 1; | ||
| 35 : | |||
| 36 : | $a = non_zero_random(-3,3,1); | ||
| 37 : | $d = non_zero_random(-3,3,1); | ||
| 38 : | $m = non_zero_random(-5,5,1); | ||
| 39 : | if ($m == 1) { $m= -0.5; } | ||
| 40 : | $b = $a * $m; | ||
| 41 : | $e = $d * $m; | ||
| 42 : | $n = non_zero_random(-5,5,1); | ||
| 43 : | if ($n == 1) { $n= -1.5; } | ||
| 44 : | $c = $a * $n; | ||
| 45 : | $ans = random(0.5, 9.5, 0.5); | ||
| 46 : | $f = $d * $n - $ans; | ||
| 47 : | |||
| 48 : | BEGIN_TEXT | ||
| 49 : | |||
| 50 : | A linear transformation \(T:{\mathbb R}^3 \rightarrow {\mathbb R}^2\) whose matrix is | ||
| 51 : | $BR | ||
| 52 : | \{ display_matrix([[$a, $b, $c], [$d, $e, "$f+k"]]) \} | ||
| 53 : | $BR | ||
| 54 : | is onto if and only if \( k \ne \)\{ans_rule(5)\}. | ||
| 55 : | |||
| 56 : | END_TEXT | ||
| 57 : | |||
| 58 : | ANS(num_cmp($ans)); | ||
| 59 : | |||
| 60 : | ENDDOCUMENT(); # This should be the last executable line in the problem. | ||
| 61 : |
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