View of /trunk/NationalProblemLibrary/Rochester/setLinearAlgebra21InnerProductSpaces/ur_la_21_1.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('dot product', 'inner product', 'norm')
    3 ##   hcao tagged and PAID on 2-20-2004
    4 ## DBsubject('Linear Algebra')
    5 ## DBchapter('Vector Spaces')
    6 ## DBsection('Inner Product')
    7 ## Date('6/3/2002')
    8 ## Author('')
    9 ## Institution('')
   10 ## TitleText1('Elementary Linear Algebra')
   11 ## EditionText1('5')
   12 ## AuthorText1('Larson, Edwards, Falvo')
   13 ## Section1('5.2')
   14 ## Problem1('')
   15 ##
   16 ##ENDDESCRIPTION
   17 
   18 DOCUMENT();        # This should be the first executable line in the problem.
   19 
   20 loadMacros(
   21 "PG.pl",
   22 "PGbasicmacros.pl",
   23 "PGchoicemacros.pl",
   24 "PGanswermacros.pl",
   25 "PGgraphmacros.pl",
   26 "PGmatrixmacros.pl",
   27 "PGnumericalmacros.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 $a = random(2,9,1);
   35 @sign = ("", "-");
   36 @sa = ($a, "(- $a)");
   37 $tag = random(0,1,1);
   38 $tag = 1;
   39 $a2 = $a * $a;
   40 $a3 = $a2 * $a;
   41 $a4 = $a3 * $a;
   42 
   43 $ans = sqrt($a2/($a2-1));
   44 
   45 BEGIN_TEXT
   46 
   47 Find the norm \( ||x|| \) of \( x=\left( 1, $sign[$tag]\frac{1}{$a}, \frac{1}{$a2},
   48   $sign[$tag]\frac{1}{$a3}, \frac{1}{$a4}, \ldots, \frac{1}{$sa[$tag] ^{n-1}}, \ldots \right) \)
   49 in \(l_2\).
   50 $BR
   51 \( ||x||= \) \{ans_rule(20)\}.
   52 
   53 END_TEXT
   54 
   55 ANS(num_cmp($ans));
   56 
   57 ENDDOCUMENT();       # This should be the last executable line in the problem.
   58