DOCUMENT();
loadMacros(
"PGstandard.pl",
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGgraphmacros.pl",
"PGmatrixmacros.pl",
"PGmorematrixmacros.pl",
"PGnumericalmacros.pl",
"PGauxiliaryFunctions.pl",
"MathObjects.pl",
"PGcourse.pl",
"MatrixCheckers.pl"
);
TEXT(beginproblem());
Context("Complex");
$i = Complex(0,1);
$one = Complex(1,0);
# define A = 2x2 random integer anti-symmetric matrix given to students
$c1 = random(1,4,1);
$c2 = random(1,5,1);
$A = new Matrix(2,2);
$A->assign(1,1, $c1 );
$A->assign(1,2, -$c2 );
$A->assign(2,1, $c2 );
$A->assign(2,2, $c1 );
# convert to matrix for display
$AMatrix = Matrix($A);
Context()->texStrings;
BEGIN_TEXT
The matrix
$BR$BR
\( $AMatrix \)
$BR$BR
has complex eigenvalues
\{ans_rule(10)\}
\( \pm \) \{ans_rule(10)\} \(i\).
$BR$BR
The eigenvectors of the matrix are
$BR
\{ mbox( ans_array(2,1,5), ans_array_extension(2,1,5) ) \}
END_TEXT
Context()->normalStrings;
ANS(Compute("$c1")->cmp);
ANS(Compute("$c2")->cmp);
ANS(basis_cmp([[1,Compute("i")],[1,Compute("-i")]]));
ENDDOCUMENT();