OK. Here is the short one (not the one I first sent you). I cut off the answers.
##DESCRIPTION
##KEYWORDS('linear albebra', 'vector space', 'linear transformation')
##
##ENDDESCRIPTION
DOCUMENT(); # This should be the first executable line in the problem.
loadMacros(
PG.pl,
PGbasicmacros.pl,
PGchoicemacros.pl,
PGanswermacros.pl,
PGgraphmacros.pl,
PGnumericalmacros.pl,
PGstatisticsmacros.pl
);
TEXT(beginproblem());
$showPartialCorrectAnswers = 1;
$d = non_zero_random(2,5,1);
$a = non_zero_random(2,5,1);
$e = $d*$a 1;
$b = non_zero_random(4,4,1);
$c = non_zero_random(4,4,1);
$f = non_zero_random(4,4,1);
$g = non_zero_random(4,4,1);
$i = non_zero_random(4,4,1);
$j = random(2,5,1);
$ans1 = ...;
$ans2 = ...;
BEGIN_TEXT
$BR
If ( T: P_1 rightarrow P_1 ) is a linear transformation such that
( T(1+$a x) = $b + $c x) and ( T($d + $e x) = $f + $g x, ) then
( T($i  $j x) = )\{ans_rule(5)}(+)\{ans_rule(5)}(x).
END_TEXT
ANS(num_cmp($ans1));
ANS(num_cmp($ans2));
ENDDOCUMENT(); # This should be the last executable line in the problem.
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