[npl] / branches / UGA / 4.3.8.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /branches/UGA/4.3.8.pg

Sat Jul 24 17:09:50 2010 UTC (2 years, 10 months ago) by ted shifrin
File size: 1508 byte(s)
Log message

    1 ## DESCRIPTION
2 ## Linear Algebra
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS ('linear algebra','vector space','basis','coordinate vector')
6 ## Tagged by cmd6a 4/29/06
7
8 ## DBsubject('Linear Algebra')
9 ## DBchapter('Vector Spaces')
10 ## DBsection('Bases')
11 ## Date('')
12 ## Author('modified by Shifrin')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGgraphmacros.pl",
28 #"PGnumericalmacros.pl",
29 #"PGstatisticsmacros.pl",
30 "PGmatrixmacros.pl"
31 );
32
33 TEXT(beginproblem());
34 $showPartialCorrectAnswers = 1; 35 36$a1 = non_zero_random(-5,5,1);
37 $a2 = non_zero_random(-10,2,1); 38$k = non_zero_random(-3,3,1);
39 $b1 =$a1 * $k; 40$d = random(1,10,1);
41 $b2 =$a2 * $k +$d;
42
43 $m = non_zero_random(-3,3,1); 44$n = random(-3,3,1);
45
46 $x1 =$a1 * $m +$b1 * $n; 47$x2 = $a2 *$m + $b2 *$n;
48
49 $RIGHT_BRACE = '\}'; 50 51 BEGIN_TEXT 52 53 The set 54 $$\mathcal B= \left\{'\{'\} \{display_matrix_mm([[a1], [a2]])\} , \{display_matrix_mm([[b1], [b2]])\} 55 \right}$$ 56 is a basis for $${\mathbb R}^2$$. 57$BR
58 Find the coordinates of the vector $$\mathbf x= \{display_matrix_mm([[x1], [x2]])\}$$ relative to the basis $$\mathcal B$$:
59 $BR 60 \{ mbox( '$$[\mathbf x]_{\mathcal B} =$$', answer_matrix(2,1,10) ) \} 61 62 END_TEXT 63 64 ANS(num_cmp($m));
65 ANS(num_cmp(\$n));
66
67
68 ENDDOCUMENT();       # This should be the last executable line in the problem.
69