View of /branches/UGA/4.3.8.pg

    1 ## DESCRIPTION
    2 ## Linear Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('linear algebra','vector space','basis','coordinate vector')
    6 ## Tagged by cmd6a 4/29/06
    7 
    8 ## DBsubject('Linear Algebra')
    9 ## DBchapter('Vector Spaces')
   10 ## DBsection('Bases')
   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 #"PGnumericalmacros.pl",
   29 #"PGstatisticsmacros.pl",
   30 "PGmatrixmacros.pl"
   31 );
   32 
   33 TEXT(beginproblem());
   34 $showPartialCorrectAnswers = 1;
   35 
   36 $a1 = non_zero_random(-5,5,1);
   37 $a2 = non_zero_random(-10,2,1);
   38 $k = non_zero_random(-3,3,1);
   39 $b1 = $a1 * $k;
   40 $d = random(1,10,1);
   41 $b2 = $a2 * $k + $d;
   42 
   43 $m = non_zero_random(-3,3,1);
   44 $n = random(-3,3,1);
   45 
   46 $x1 = $a1 * $m + $b1 * $n;
   47 $x2 = $a2 * $m + $b2 * $n;
   48 
   49 $RIGHT_BRACE = '\}';
   50 
   51 BEGIN_TEXT
   52 
   53 The set
   54 \( \mathcal B= \left\{'\{'\} \{display_matrix_mm([[$a1], [$a2]])\} , \{display_matrix_mm([[$b1], [$b2]])\}
   55 \right}\)
   56 is a basis for \( {\mathbb R}^2 \).
   57 $BR
   58 Find the coordinates of the vector \(\mathbf x= \{display_matrix_mm([[$x1], [$x2]])\} \) relative to the basis \( \mathcal B \):
   59 $BR
   60 \{ mbox( '\( [\mathbf x]_{\mathcal B} = \)', answer_matrix(2,1,10) ) \}
   61 
   62 END_TEXT
   63 
   64 ANS(num_cmp($m));
   65 ANS(num_cmp($n));
   66 
   67 
   68 ENDDOCUMENT();       # This should be the last executable line in the problem.
   69