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# View of /trunk/NationalProblemLibrary/Rochester/setLinearAlgebra15TransfOfLinSpaces/ur_la_15_7.pg

Sun Mar 26 15:53:04 2006 UTC (7 years, 1 month ago) by jj
File size: 986 byte(s)
```Initial import
```

```    1 ##DESCRIPTION
2 ##KEYWORDS('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 "PGmatrixmacros.pl",
15 "PGnumericalmacros.pl",
16 "PGauxiliaryFunctions.pl"
17 );
18
19 TEXT(beginproblem());
21
22 \$a = random(2,9,1);
23 \$b = random(2,9,1);
24 if (\$b == \$a) { \$b = \$b+1; }
25
26 \$c = 2*\$a;
27
28 BEGIN_TEXT
29
30 Find the matrix \(A\) of the linear transformation \(T(f(t)) = \$a f'(t) + \$b f(t)\) from \(P_2\) to \(P_2\) with
31 respect to the standard basis for \(P_2\), \( \$LB 1, t, t^2 \$RB \).
32 \$BR
33 \{ mbox( '\(A=\)', answer_matrix(3,3,5) ) \}
34
35 END_TEXT
36
37 ANS(num_cmp(\$b));
38 ANS(num_cmp(\$a));
39 ANS(num_cmp(0));
40
41 ANS(num_cmp(0));
42 ANS(num_cmp(\$b));
43 ANS(num_cmp(\$c));
44
45 ANS(num_cmp(0));
46 ANS(num_cmp(0));
47 ANS(num_cmp(\$b));
48
49
50 ENDDOCUMENT();       # This should be the last executable line in the problem.
51
```