## DESCRIPTION ## Linear Algebra ## ENDDESCRIPTION ## KEYWORDS('matrix' 'determinant') ## Tagged by tda2d ## DBsubject('Linear Algebra') ## DBchapter('Matrices') ## DBsection('Properties of Determinants') ## Date('') ## Author('edited by Shifrin') ## Institution('TCNJ') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGgraphmacros.pl", "PGmatrixmacros.pl", "PGnumericalmacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$det1 = non_zero_random(-5,5,1); $k = random(2,9,1)*random(-1,1,2);$j = random(2,9,1)*random(-1,1,2); $ans1 =$det1*$k;$ans2 = $det1*$j; $ans3 = -$det1; $str1 =$str1 . "$k";$str1 = $str1 . "c";$str2 = $str2 . "$k"; $str2 =$str2 . "f"; $str3 =$str3 . "$k";$str3 = $str3 . "i";$str4 = $str4 . "$j"; $str4 =$str4 . "b"; $str5 =$str5 . "$j";$str5 = $str5 . "e";$str6 = $str6 . "$j"; $str6 =$str6 . "h"; BEGIN_TEXT Given $$\left| \begin{matrix} a&b&c\\d&e&f\\g&h&i \end{matrix}\right|=det1$$, find the following determinants. $PAR $$\left| \begin{matrix}a&b&str1\\ d&e&str2 \\ g&h&str3 \end{matrix} \right|= \$$ \{ans_rule(5)\}$PAR $$\left| \begin{matrix} a&str4&c\\ d&str5&f \\ g&str6&i\end{matrix}\right| = \$$ \{ans_rule(5) \} $PAR $$\left|\begin{matrix} c&b&a \\ f&e&d \\ i&h&g\end{matrix}\right|= \$$ \{ans_rule(5) \} END_TEXT ANS(num_cmp($ans1)); ANS(num_cmp($ans2)); ANS(num_cmp($ans3)); ENDDOCUMENT(); # This should be the last executable line in the problem.