[npl] / trunk / NationalProblemLibrary / Rochester / setLinearAlgebra14TransfOfRn / ur_la_14_6.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# Annotation of /trunk/NationalProblemLibrary/Rochester/setLinearAlgebra14TransfOfRn/ur_la_14_6.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 : 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 :