View of /trunk/NationalProblemLibrary/TCNJ/TCNJ_LengthOrthogonality/problem4.pg

    1 ## DESCRIPTION
    2 ## Linear Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('inner product' 'orthogonal')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Linear Algebra')
    9 ## DBchapter('Vector Spaces')
   10 ## DBsection('Inner Product')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('TCNJ')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 
   21 DOCUMENT();        # This should be the first executable line in the problem.
   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 "PGcomplexmacros.pl"
   33 );
   34 
   35 TEXT(beginproblem());
   36 # Do not show which answers are incorrect.
   37 $showPartialCorrectAnswers = 1;
   38 
   39 $n = non_zero_random(-4,4,2);
   40 $m = non_zero_random(-5,5,2);
   41 
   42 $w1 = random(-9,9,2);
   43 $w2 = random(-8,8,2);
   44 $w3 = random(-9,9,1);
   45 
   46 $x1 = - $n;
   47 $x2 = - $n;
   48 $x3 = $n;
   49 
   50 $y1 = random(-8,8,2);
   51 $y2 = random(-9,9,2);
   52 $y3 = random(-9,9,1);
   53 
   54 $z1 = - $m;
   55 $z2 = - $m;
   56 $z3 = $m;
   57 
   58 # Make a new checkbox multiple choice
   59 $tf = new_pop_up_select_list();
   60 $tf->ra_pop_up_list(["?"=>"Select an Answer", "Yes" => "Yes", "No" => "No"]);
   61 # $cmc now "contains" the checkbox multiple choice object.
   62 
   63 # Insert some  questions and matching answers in the q/a list
   64 
   65 $tf -> qa (
   66 
   67 mbox( '\( v = \)', display_matrix([[$w1], [$w2], [$w3]]) ),
   68 "No",
   69 
   70 mbox( '\( v = \)', display_matrix([[$x1], [$x2], [$x3]]) ),
   71 "Yes",
   72 
   73 mbox( '\( v = \)', display_matrix([[$y1], [$y2], [$y3]]) ),
   74 "No",
   75 
   76 mbox( '\( v = \)', display_matrix([[$z1], [$z2], [$z3]]) ),
   77 "Yes",
   78 );
   79 
   80 $tf->choose(3);
   81 
   82 # Insert some incorrect answers
   83 
   84 # Print the text using $mc->print_q for the questions and
   85 # $mc->print_a to print the answers.
   86 BEGIN_TEXT
   87 
   88 \{ mbox( 'Let \(W\) be the set of all vectors ', display_matrix([['x'], ['y'], ['x + y']]), 'with \(x\) and \(y\) real.'  ) \}
   89 $BR
   90 Determine whether each of the following vectors is in \(W^{\perp}\).
   91 $BR
   92 $BR
   93 
   94  \{ $tf -> print_q \}
   95 
   96 END_TEXT
   97 
   98 # Enter the correct answers to be checked against the answers to the students.
   99 ANS(str_cmp( $tf->ra_correct_ans )   ) ;
  100 
  101 ENDDOCUMENT();