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MatrixCheckers.pl

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.)

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-<gt`

ans_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).

Paul Pearson, Hope College, Department of Mathematics