View of /trunk/NationalProblemLibrary/Rochester/setLinearAlgebra11Eigenvalues/ur_la_11_14.pg

    1 ## DESCRIPTION
    2 ## Linear Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('linear algebra','matrix','eigenvalue')
    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 "PGmorematrixmacros.pl"
   32 );
   33 
   34 TEXT(beginproblem());
   35 $showPartialCorrectAnswers = 1;
   36 
   37 $a = non_zero_random(-8,8,1);
   38 $b = non_zero_random(-9,9,1);
   39 $c = non_zero_random(-8,8,1);
   40 if ($a == $c) { $c=9; }
   41 
   42 $k = - ($a - $c)**2/(4*$b);
   43 
   44 BEGIN_TEXT
   45 
   46 For which value of \(k\) does the matrix
   47 $BR
   48 \{ mbox( '\(A=\)', display_matrix([[$a, 'k'], [$b, $c]]) )\}
   49 $BR
   50 have one real eigenvalue of multiplicity \(2\)?
   51 $BR
   52 \(k=\) \{ans_rule(20)\}.
   53 
   54 END_TEXT
   55 
   56 ANS(num_cmp($k));
   57 
   58 ENDDOCUMENT();       # This should be the last executable line in the problem.
   59