ard.pl",
  "PGchoicemacros.pl",
  "PGgraphmacros.pl",
  "PGmatrixmacros.pl",
  "PGnumericalmacros.pl",
  "PGmorematrixmacros.pl",
  "MathObjects.pl",
  "freemanMacros.pl",
  "PGasu.pl",
  "PGcourse.pl"
);

# make sure we're in the context we want
Context("Numeric");
$v11=random(1,9,1);
$v12=random(-9,9,1);
$v13=random(-9,9,1);
$v21=random(-9,9,1);
$v22=random(1,9,1);
$v23=random(-9,9,1);
if($v11*$v22==$v12*$v21){$v22=-$v22;}
$v31=random(1,9,1)*random(-1,1,2);
$v32=random(-9,9,1);
$v33=random(1,9,1);
if($v11*$v22*$v33+$v21*$v32*$v13+$v31*$v12*$v23-$v13*$v22*$v31-$v23*$v32*$v11-$v33*$v12*$v21==0){$v33=-$v33;}
$v41=random(1,9,1)*random(-1,1,2);
$v42=random(1,9,1)*random(-1,1,2);
$v43=random(1,9,1)*random(-1,1,2);

$a1=random(1,9,1);
$a2=random(1,9,1)*random(-1,1,2);
$a3=random(1,9,1)*random(-1,1,2);

$a=($v42-$a2*$v22-$a3*$v32)/$a1;
$b=($v41-$a1*$v11-$a2*$v21)/$a3;

$m[1][1]=$v11;
$m[1][2]=$v12;
$m[1][3]=$v13;
$m[2][1]=$v21;
$m[2][2]=$v22;
$m[2][3]=$v23;
$m[3][1]=$v31;
$m[3][2]=$v32;
$m[3][3]=$v33;
$m[4][1]=$v41;
$m[4][2]=$v42;
$m[4][3]=$v43;



TEXT(beginproblem());
$showPartialCorrectAnswers = 1;
BEGIN_TEXT
\{ textbook_ref_exact("Holt Linear Algebra", "2.1","12") \} 
$PAR
Express the following system of linear equations as a vector equation. 
$PAR
\[$v11 x_1 + $v21 x_2 + $v31 x_3 = $v41\] 
$PAR
\[$v12 x_1 + $v22 x_2 + $v32 x_3 = $v42\] 
$PAR
\[$v13 x_1 + $v23 x_2 + $v33 x_3 = $v43\] 
$PAR
$PAR
\{ mbox( 
display_matrix([[ans_rule(5)],[ans_rule(5)],[ans_rule(5)]]), '\(x_1 +\) ', 
display_matrix([[ans_rule(5)],[ans_rule(5)],[ans_rule(5)]]), '\(x_2 +\)', 
display_matrix([[ans_rule(5)],[ans_rule(5)],[ans_rule(5)]]), '\(x_3 =\)', 
display_matrix([[ans_rule(5)],[ans_rule(5)],[ans_rule(5)]]) 
) \}
$PAR
END_TEXT
Context()->normalStrings;

$showPartialCorrectAnswers = 1;

foreach $i (0..3) {

   foreach $j (0..2) {
   		ANS(num_cmp($m[$i+1][$j+1])  );
   	}
}


Context()->texStrings;
SOLUTION(EV3(<<'END_SOLUTION'));
$PAR 
SOLUTION 
$PAR

\[
\left[\begin{matrix} $v11 \cr $v12 \cr $v13 \cr \end{matrix} \right] x_1+
\left[\beg