View of /branches/UGA/1.4.10.pg

    1 ## DESCRIPTION
    2 ##   Matrix Transpose and Dot Product
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Transpose', 'Dot Product')
    6 
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vectors and the Geometry of Space')
   10 ## DBsection('Matrix Algebra')
   11 ## Date('6/11/10')
   12 ## Author('Ted Shifrin'
   13 ## Institution('UGA')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 
   22 loadMacros("PG.pl",
   23            "PGbasicmacros.pl",
   24            "PGchoicemacros.pl",
   25            "PGanswermacros.pl",
   26            "PGauxiliaryFunctions.pl",
   27            "PGmatrixmacros.pl",
   28            "PGmorematrixmacros.pl",
   29            "Parser.pl",
   30            "MathObjects.pl",
   31            );
   32 
   33 TEXT(beginproblem());
   34 $showPartialCorrectAnswers = 1;
   35 
   36 
   37 Context("Vector");
   38 
   39 
   40 $a = non_zero_random(-3,3);
   41 $b = non_zero_random(-3,3);
   42 $c = non_zero_random(-3,3);
   43 $d = non_zero_random(-3,3);
   44 
   45 $n = random(3,7);
   46 
   47 $P = ColumnVector("<$a,$b>");
   48 $Q = ColumnVector("<$c,$d>");
   49 
   50 $ans = Real("$P.$Q");
   51 
   52 
   53 Context()->texStrings;
   54 
   55 BEGIN_TEXT
   56 
   57 Suppose \(A\) is a \(2\times $n\) matrix, and \(\mathbf x\in\mathbb R^{$n}\) and \(\mathbf y\in\mathbb R^2\) are vectors.
   58 $PAR
   59 If \(A\mathbf x = $P\) and \(\mathbf y = $Q\), compute
   60 
   61 $PAR
   62 
   63 \{mbox('\(A^T\mathbf y \cdot \mathbf x =\)', ans_rule(8))\}
   64 $PAR
   65 
   66 END_TEXT
   67 ANS($ans->cmp);
   68 
   69 ENDDOCUMENT();