View of /branches/UGA/9.3.4.pg

    1 ## DESCRIPTION
    2 ## Linear Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('linear algebra','matrix','power','diagonalizable')
    6 ## Tagged by cmd6a 4/30/06
    7 
    8 ## DBsubject('Linear Algebra')
    9 ## DBchapter('Matrices')
   10 ## DBsection('Diagonalization')
   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 
   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 = non_zero_random(-2,2,1);
   37 $b = 2/$a;
   38 $s = random(-1,1,2);
   39 $c = random(2,9,1);
   40 $d = random(2,9,1);
   41 if ($c == $d) {$d = $d+1;}
   42 
   43 $m11 = 2*$c-$d;
   44 $m12 = $s*$a*$d - $s*$a*$c;
   45 $m21 = $s*$b*$c - $s*$b*$d;
   46 $m22 = 2*$d - $c;
   47 
   48 $ans11 = "2*($c**n) - $d**n";
   49 $ans12 = "$s*$a*($d**n) - $s*$a*($c**n)";
   50 $ans21 = "$s*$b*($c**n) - $s*$b*($d**n)";
   51 $ans22 = "2*($d**n) - $c**n";
   52 
   53 BEGIN_TEXT
   54 
   55 Let \(M = \{display_matrix_mm([[$m11, $m12], [$m21, $m22]]) \}\).
   56 $BR
   57 Find formulas for the entries of \(M^n\), where \(n\) is a positive integer.
   58 $BR
   59 \{ mbox( '\(M^n=\)', answer_matrix(2,2,20), '.' ) \}
   60 
   61 END_TEXT
   62 
   63 ANS(fun_cmp($ans11, vars=>'n'));
   64 ANS(fun_cmp($ans12, vars=>'n'));
   65 ANS(fun_cmp($ans21, vars=>'n'));
   66 ANS(fun_cmp($ans22, vars=>'n'));
   67 
   68 ENDDOCUMENT();       # This should be the last executable line in the problem.
   69