[npl] / trunk / NationalProblemLibrary / Rochester / setLinearAlgebra21InnerProductSpaces / ur_la_21_1.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Thu Aug 16 23:07:34 2007 UTC (5 years, 9 months ago) by jj
File size: 1245 byte(s)
Moved problems back into place in the Rochester library, and set up
redirect files from their former locations.


    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
21 "PG.pl",
22 "PGbasicmacros.pl",
23 "PGchoicemacros.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