NAME

MatrixCheckers.pl

SYNOPSIS

Provides subroutines for answer checking using MathObjects matrices with real entries. (Sadly, it does not provide routines for using matrices to win at the game of checkers.)

DESCRIPTION

First, load the MatrixCheckers.pl macro file. If the basis has more than one vector, also load parserMultiAnswer.pl.

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

For a matrix that has a single column or row, the way to use the answer checkers is the same as using a custom answer checker inside of cmp(checker=~~&name_of_answer_checker_subroutine)> such as

ANS( Matrix([[1],[2],[3]])-cmp( checker=>~~&basis_checker_one_column ) );>

ANS( Matrix([[1],[2],[3]])-cmp( checker=>~~&unit_basis_checker_one_column ) );>

The "one column" at the end of the checker name refers to the fact that the student answer is a one-column matrix. The "unit basis checker" ensures that the student answer has unit length.

For answers that are a collection of column or row vectors, the way to use the answer checkers is inside of a MultiAnswer object. The macro parserMultiAnswer.pl should also be loaded. The answer checkers that should be used inside a MultiAnswer object are:

basis_checker_columns

orthonormal_basis_checker_columns

basis_checker_rows

orthonormal_basis_checker_rows

parametric_plane_checker_columns

Here is an example of how to use these answer checkers. In the setup section of the PG file we create two 3 x 1 MathObject matrices with real-entries that serve as basis vectors. The object $multians takes the basis vectors as input and passes them to the custom answer checker called by checker =<gt...>.

$basis1 = Matrix([1/sqrt(2), 0, 1/sqrt(2)])->transpose;
$basis2 = Matrix([0,1,0])->transpose;

$multians = MultiAnswer($basis1, $basis2)->with(
    singleResult => 1,
    separator => ', ',
    tex_separator => ', ',
    allowBlankAnswers=>0,
    checker => ~~&orthonormal_basis_checker_columns,
);

In the main text portion of the PG file, we use \{ $multians-<gtans_array(15) \}> to create an array of text boxes that are 15 characters wide and have square brackets around them to look like a matrix. The braces around the vectors, which are produced by \(\Bigg\lbrace\) and \(\Bigg\rbrace\), are a matter of personal preference (since a basis is an ordered set, I like to include braces).

Context()->texStrings;
BEGIN_TEXT
Find an orthonormal basis for...
$BR
$BR
$BCENTER
\(\Bigg\lbrace\)
\{ $multians->ans_array(15) \},
\{ $multians->ans_array(15) \}
\(\Bigg\rbrace.\)
$ECENTER
END_TEXT
Context()->normalStrings;

The answer evaluation section of the PG file is totally standard.

ANS( $multians->cmp );

The parametric_plane_checker_columns should be used for solutions to non-homogeneous systems of linear equations for which the solution is essentially a point plus the span of several linearly independent vectors. When using the parametric plane checker, the first vector input always serves as a point on the hyperplane (i.e., the first vector input is always a particular solution), while the remaining vectors are a basis for the hyperplane (i.e., they span the homogeneous solution set).

AUTHORS

Paul Pearson, Hope College, Department of Mathematics