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Sun Mar 26 15:53:04 2006 UTC (7 years, 1 month ago) by jj
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Initial import


    1 ##DESCRIPTION
2 ##KEYWORDS('linear albebra', 'vector space', 'linear transformation', 'matrix', 'basis')
3 ##
4 ##ENDDESCRIPTION
5
6 DOCUMENT();        # This should be the first executable line in the problem.
7
9 "PG.pl",
10 "PGbasicmacros.pl",
11 "PGchoicemacros.pl",
13 "PGgraphmacros.pl",
14 "PGnumericalmacros.pl",
15 "PGstatisticsmacros.pl",
16 "PGmatrixmacros.pl"
17 );
18
19 TEXT(beginproblem());
20 $showPartialCorrectAnswers = 1; 21 22$a = random(2,15,1);
23 $b = random(2,15,1); 24 while ($a == $b) {$b = random(2,15,1); }
25
26 BEGIN_TEXT
27
28 \{ mbox( 'The matrices $$A_1=$$', display_matrix([[1, 0], [0, 0]]), ', ',
29    ' $$A_2=$$', display_matrix([[0, 1], [0, 0]]), ',' ) \}
30 $BR 31 \{ mbox( '$$A_3=$$', display_matrix([[0, 0], [1, 0]]), ', ', 32 ' and $$A_4=$$', display_matrix([[0, 0], [0, 1]]) ) \} 33$BR
34 form a basis for the linear space $$V={\mathbb R}^{2\times 2}.$$
35 Write the matrix of the linear transformation $$T:{\mathbb R}^{2\times 2} \rightarrow {\mathbb R}^{2\times 2}$$
36 such that $$T(A)=a A + b A^T$$ relative to this
37 basis:
38 $BR 39 \{ answer_matrix(4,4,5) \} 40 41 END_TEXT 42 43$c = $a+$b;
44
45 ANS(num_cmp($c)); 46 ANS(num_cmp(0)); 47 ANS(num_cmp(0)); 48 ANS(num_cmp(0)); 49 ANS(num_cmp(0)); 50 ANS(num_cmp($a));
51 ANS(num_cmp($b)); 52 ANS(num_cmp(0)); 53 ANS(num_cmp(0)); 54 ANS(num_cmp($b));
55 ANS(num_cmp($a)); 56 ANS(num_cmp(0)); 57 ANS(num_cmp(0)); 58 ANS(num_cmp(0)); 59 ANS(num_cmp(0)); 60 ANS(num_cmp($a+\$b));
61
62
63 ENDDOCUMENT();       # This should be the last executable line in the problem.
64