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

    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 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.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