[npl] / trunk / NationalProblemLibrary / Rochester / setLinearAlgebra11Eigenvalues / ur_la_11_12.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/Rochester/setLinearAlgebra11Eigenvalues/ur_la_11_12.pg

Tue May 2 20:24:19 2006 UTC (7 years ago) by jjholt
File size: 1153 byte(s)
Update tags.


    1 ## DESCRIPTION
2 ## Linear Algebra
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS ('linear algebra','matrix','eigenvalue','determinant','trace')
6 ## Tagged by cmd6a 4/30/06
7
8 ## DBsubject('Linear Algebra')
9 ## DBchapter('Matrices')
10 ## DBsection('Eigenvalues')
11 ## Date('')
12 ## Author('')
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 "PGmatrixmacros.pl",
29 "PGnumericalmacros.pl",
30 "PGauxiliaryFunctions.pl"
31 );
32
33 TEXT(beginproblem());
34 $showPartialCorrectAnswers = 1; 35 36$a = random(-10,5,1);
37 $b = random($a+1,10,1);
38
39 $tr =$a+$b; 40$det = $a*$b;
41
42 BEGIN_TEXT
43
44 Suppose that the trace of a $$2\times 2$$ matrix $$A$$ is $${\rm tr}(A)=tr$$, and the determinant is
45 $${\rm det}(A)=det$$. Find the eigenvalues of $$A$$.
46 $BR 47 smaller eigenvalue = \{ans_rule(5)\}, 48$BR
49 larger eigenvalue = \{ans_rule(5)\}.
50
51 END_TEXT
52
53 ANS(num_cmp($a)); 54 ANS(num_cmp($b));
55
56 ENDDOCUMENT();       # This should be the last executable line in the problem.
57