## 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.