## DESCRIPTION
## Linear Algebra
## ENDDESCRIPTION

## Tagged by tda2d

## DBsubject(Linear algebra)
## DBchapter(Euclidean spaces)
## DBsection(Linear combinations)
## Date(July 2013)
## Institution(TCNJ and Hope College)
## Author(Paul Pearson)
## Level(2)
## MO(1)
## TitleText1('Linear Algebra with Applications')
## AuthorText1('Jeffrey Holt')
## EditionText1('1')
## Section1('2.1')
## Problem1('')
## KEYWORDS('vector' 'line' 'parametric')

DOCUMENT();

loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "parserMultiAnswer.pl",
  "MatrixCheckers.pl",
  "PGcourse.pl"
);

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

Context('Matrix')->variables->are('x'=>'Real');

$m = random(-1,1,2) * random(2,9,1);
$b = non_zero_random(-9,9,1);

$y = Formula("$m x + $b")->reduce;

$displace = Matrix([0,$b])->transpose;
$basis1 = Matrix([1,$m])->transpose;

$multians = MultiAnswer($displace, $basis1)->with(
  singleResult => 1,
  separator => ', ',
  tex_separator => ', ',
  allowBlankAnswers=>0,
  checker => ~~&parametric_plane_checker_columns,
);

Context()->texStrings;
BEGIN_TEXT
Let \( L \) be the line \( y = $y \) in \( \mathbb{R}^2 \).
Find vectors \( \vec{a} \) and \( \vec{b} \) so that
\( \vec{v} = \vec{a} + t \vec{b} \) is a parametric
equation for \( L \).
$BR
$BR
\( \vec{v} = \)
\{ $multians->ans_array \}
\( + t \)
\{ $multians->ans_array \}.
END_TEXT
Context()->normalStrings;


ANS($multians->cmp);
;
ENDDOCUMENT();
