## DESCRIPTION
## Linear Algebra
## ENDDESCRIPTION

## KEYWORDS ('linear algebra','linear system')
## Tagged by cmd6a 5/3/06

## DBsubject('Linear Algebra')
## DBchapter('Systems of Linear Equations and Matrices')
## DBsection('Introduction to Systems of Linear Equations')
## 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",
"PGauxiliaryFunctions.pl"

);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a11 = random(2,6,2) * random(-1,1,2);
$a12 = random(3,5,1) * random(-1,1,2);
$a13 = random(3,5,2) * random(-1,1,2);
$a21 = random(3,5,2) * random(-1,1,2);
$a22 = random(2,6,2) * random(-1,1,2);
$a23 = random(2,6,2) * random(-1,1,2);
$a31 = random(2,6,1) * random(-1,1,2);
$a32 = random(3,5,2) * random(-1,1,2);
$a33 = random(2,6,2) * random(-1,1,2);

$x = random(-5,5,1);
$y = random(-5,5,1);
$z = random(-5,5,1);

$b1 = $a11*$x + $a12*$y + $a13*$z;
$b2 = $a21*$x + $a22*$y + $a23*$z;
$b3 = $a31*$x + $a32*$y + $a33*$z;

$NO_SPACE = '@{}';


BEGIN_TEXT

Solve the system using matrices (row operations) $BR
\[ \left\{ "\{"; \}
\begin{array}{r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r}
               $a11 x & +$a12 y & +$a13 z &=& $b1 \cr
	        $a21 x & +$a22 y & +$a23 z &=& $b2 \cr
               $a31 x & +$a32 y & +$a33 z &=& $b3 
\end{array}\right. \]
$BR
\(x = \) \{ans_rule(5)\}
$BR
\(y = \) \{ans_rule(5)\}
$BR
\(z = \) \{ans_rule(5)\}

END_TEXT
ANS(num_cmp($x, mode=>"arith"));
ANS(num_cmp($y, mode=>"arith"));
ANS(num_cmp($z, mode=>"arith"));

ENDDOCUMENT();       # This should be the last executable line in the problem.