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# View of /branches/UGA/1.4.10.pg

Revision 1457 - (download) (annotate)
Sat Jul 24 17:09:50 2010 UTC (2 years, 10 months ago) by ted shifrin
File size: 1315 byte(s)
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    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();


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