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

    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 
    8 loadMacros(
    9 "PG.pl",
   10 "PGbasicmacros.pl",
   11 "PGchoicemacros.pl",
   12 "PGanswermacros.pl",
   13 "PGgraphmacros.pl",
   14 "PGmatrixmacros.pl",
   15 "PGnumericalmacros.pl",
   16 "PGauxiliaryFunctions.pl"
   17 );
   18 
   19 TEXT(beginproblem());
   20 $showPartialCorrectAnswers = 1;
   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