## DESCRIPTION
## Linear Algebra
## ENDDESCRIPTION

## KEYWORDS('bases' 'basis' 'matrix' 'linearly independent')
## Tagged by tda2d

## DBsubject('Linear Algebra')
## DBchapter('Vector Spaces')
## DBsection('Bases')
## Date('')
## Author('modified by Shifrin')
## Institution('TCNJ')
## 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",
"MathObjects.pl"
);

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

Context("Vector");

$x = ColumnVector(-2,3,0);
$y = ColumnVector(6,-1,5);

# Make a new checkbox multiple choice 
$cmc1 = new_checkbox_multiple_choice(); 
# $cmc now "contains" the checkbox multiple choice object. 

# Insert some  questions and matching answers in the q/a list 
$cmc1 -> qa (
             "Determine if \(W\) is a basis for \( {\mathbb R}^3\) and check the correct answer(s) below.",
        " \(W\) is not a basis because it does not span \( {\mathbb R}^3\).",
);

# Insert some incorrect answers 
$cmc1 -> extra(  
        " \(W\) is a basis.",               
        " \(W\) is not a basis because it is linearly dependent.",
);

Context()->texStrings;
BEGIN_TEXT

Let \(W\) be the set \(\left\{"\{"\} $x, $y \right\} \).
$PAR
\{$cmc1 -> print_q \}
$BR
\{$cmc1 -> print_a \}

END_TEXT

ANS(checkbox_cmp( $cmc1->correct_ans )   ) ;

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