## DESCRIPTION ## Linear Algebra ## ENDDESCRIPTION ## KEYWORDS ('linear algebra','matrix','singular value','eigenvalue') ## Tagged by cmd6a 5/3/06 ## DBsubject('Linear Algebra') ## DBchapter('Matrices') ## DBsection('Eigenvalues') ## Date('') ## Author('') ## Institution('Rochester') ## 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", "PGmorematrixmacros.pl", "PGcomplexmacros.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$ans1 = random(5,9,1); $ans2 = random(1,4,1);$a = $ans1 * random(-1,1,2); if ($a < 0) { $b =$ans2 * random(-1,1,2); } else { $b = -$ans2; } BEGIN_TEXT Find the singular values $$\sigma_1 \ge \sigma_2$$ of $BR \{ mbox( '$$A=$$', display_matrix([[$a, 0], [0, $b]]), '.' ) \}$BR $$\sigma_1 =$$ \{ans_rule(10)\}, $BR $$\sigma_2 =$$ \{ans_rule(10)\}. END_TEXT ANS(num_cmp($ans1)); ANS(num_cmp(\$ans2)); ENDDOCUMENT(); # This should be the last executable line in the problem.