## DESCRIPTION
## Linear Algebra
## ENDDESCRIPTION

## KEYWORDS ('linear algebra','eigenvalues', 'diagonalizability')

## DBsubject('Multivariable Mathematics')
## DBchapter('Linear Transformations')
## DBsection('Eigenvalues and Eigenvectors, Diagonalizability')
## Date('March 13, 2010')
## Author('Shifrin')
## Institution('UGA')
## 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",
           "PGauxiliaryFunctions.pl",
           "PGmatrixmacros.pl",
           "PGmorematrixmacros.pl",
           "Parser.pl",
           "weightedGrader.pl"
           );


TEXT(beginproblem());
$showPartialCorrectAnswers = 0;

install_weighted_grader();

Context("Matrix");

$a=random(-3,3);
$b=non_zero_random(-3,3);
do{$c=random(-3,3)} until ($c!=$a);
do{$d=random(-3,3)} until ($d!=$a && $d!=$c);
do{$e=random(-3,3)} until ($e!=$a && $e!=$c && $e!=$d);
$r1=random(-5,5);
$r2=random(-5,5);
$r3=random(-5,5);
$r4=non_zero_random(-5,5);
$r5=random(-5,5);
$r6=random(-5,5);


$M1 = Matrix("[[$a,$b,$r1,$r2],[0,$a,$r3,$r4],[0,0,$c,$r5],[0,0,0,$d]]");
$M2 = Matrix("[[$a,0,0,0],[$r1,$c,0,0],[$r2,$r3,$d,0],[$r4,$r5,$r2,$e]]");
$M3 = Matrix("[[$a,$r1,0,$r2],[0,$c,0,0],[0,$r4,$a,$r5],[0,0,0,$c]]");
$M4 = Matrix("[[$a,$r3,$r2,$r1],[$r3,$a,$r5,$r4],[$r2,$r5,$c,$r6],
[$r1,$r4,$r6,$d]]");


@Ms = ($M1,$M2,$M3,$M4);
@diags=('not diagonalizable','diagonalizable','diagonalizable','diagonalizable'); 

@choice=NchooseK(4,4);
@A=@Ms[@choice];
@diag=@diags[@choice];

$ans1=str_cmp($diag[0]);
$ans2=str_cmp($diag[1]);
$ans3=str_cmp($diag[2]);
$ans4=str_cmp($diag[3]);



Context()->texStrings;
BEGIN_TEXT

Consider the matrices 
\[A = $A[0], \quad B = $A[1], \] 
$BR
\[C = $A[2], \quad D = $A[3] . \]
 
$PAR
The matrix \(A\) is \{pop_up_list(['?','diagonalizable','not diagonalizable'])\}.
$PAR
The matrix \(B\) is \{pop_up_list(['?','diagonalizable','not diagonalizable'])\}.
$PAR
The matrix \(C\) is \{pop_up_list(['?','diagonalizable','not diagonalizable'])\}.
$PAR
The matrix \(D\) is \{pop_up_list(['?','diagonalizable','not diagonalizable'])\}.
$PAR

END_TEXT

ANS($ans1,$ans2,$ans3,$ans4);

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