Matrix Answer Alternative

DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');

Context('Matrix');

$example1 = Matrix([ [ 1, 2, 3 ], [ 4, 5, 6 ] ]);
$example2 = $example1->column(1);
$example3 = $example1->row(1);

BEGIN_PGML
The purpose of this question is to show you the syntax needed to enter matrices
in WeBWorK when there is only one answer box for entering a matrix (which is not
obvious) or when there are multiple answer boxes for entering a matrix (which is
obvious).  The examples below should be self-explanatory, so you can jump to
them if you want; however, a detailed explanation follows if you want to read
more.

Matrices use square brackets to enclose items in lists.  A matrix with one row,
such as a row vector, is a comma separated list enclosed by square brackets.  A
matrix with more than one row or a column vector is a comma separated list of
lists, where each list uses square brackets to enclose its items.  Your answers
must use square brackets to enclose each row in a matrix or in a column vector.
Also, a pair of square brackets is needed to enclose a matrix with more than one
row (e.g., a [`2 \times 3`] matrix and a [`2 \times 1`] column vector have
multiple rows so they need extra square brackets, but a [`1 \times 3`] row
vector has only one row so it does not need extra square brackets).  Your
answers may have spaces and line breaks in them, such as

>> [| [ [1, 2, 3], |] <<
>> [| [4, 5, 6] ]  |] <<

+ Enter the matrix [``[$example1]``] as [@ $example1->string @]*
[@ ans_box(3,30) @]*

+ Enter the column vector [``[$example2]``] as [@ $example2->string @]*
[@ ans_box(3,30) @]*

+ Enter the row vector [``[$example3]``] as [@ $example3->string @]*
[@ ans_box(3,30) @]*
END_PGML

ANS($example1->cmp);
ANS($example2->cmp);
ANS($example3->cmp);

Context('Matrix');

$example4 = Matrix([ [ 1, 2, 3 ], [ 4, 5, 6 ] ]);

BEGIN_PGML
[$BR]*
+ Entering a matrix using multiple answer blanks is straightforward --
just put each matrix entry into its own answer blank.
Enter the matrix [`` [$example4] ``] with one matrix entry per answer box.
[______]*{$example4}
END_PGML

ENDDOCUMENT();