Hi Justin,
Please see if this works as expected:
<problem>
<startouttext />
Give an example of an idempotent matrix<br />
<endouttext />
<customresponse>
<answer type="loncapa/perl"># Get rid of white space
$submission=~s/\s+//gs;
# It's not a matrix if it does not at have parentheses
unless ($submission=~/^\(.+\)$/) { return 'BAD_FORMULA'; }
# Now evaluate something in MAXIMA
$determinant=&cas('maxima','rank(matrix'.$submission.'^^2-matrix'.$submission.')');
# If we get error, there was some syntax problem
if ($determinant=~/Error/i) { return 'BAD_FORMULA'; }
# Test the outcome of the MAXIMA expression
if ($determinant==0) { return 'EXACT_ANS'; }
return 'INCORRECT';</answer>
<textline readonly="no" spellcheck="none" size="80" />
</customresponse>
</problem>
- Gerd.
> On May 25, 2015, at 9:49 PM, Justin Gray <jg...@math.sfu.ca> wrote:
>
> I would appreciate it if someone could assist me with coding the following
> problem.
>
> Give an example of an idempotent matrix.
>
> Ideally, I would like students to input their answer using the format
> (row_1,...,row_m) using a matrix of any size, so that ([1,1],[0,0]) and
> ([2,-2,-4],[-1,3,4],[1,-2,-3]) would both be acceptable answers.
> (A matrix A is idempotent if A^2=A.)
>
> If I understand correctly, using a mathresponse problem is problematic in
> this case because there is some preprocessing of the students submission that
> makes it difficult to use in the answer algorithm, but one way around this is
> to use customresponse combined with the &cas() function.
>
> In order that Maxima understands the students submission, the expression
> 'matrix' needs to be appended to the front. Also, matrix exponentiation is
> denoted by A^^n in Maxima. If it is easier to test a numerical condition, one
> could verify that rank(A^^2 - A) = 0.
>
> Thanks,
> Justin
>
> P.S. Ideally, I would like to stipulate that students provide a nontrivial
> example (excluding the zero matrix and the identity matrix) but that is the
> topic of another discussion.
>
>
>
> Justin Gray | Senior Lecturer
> Department of Mathematics | Simon Fraser University
> 8888 University Drive, Burnaby | V5A 1S6 | Canada
> Tel: +1 778.782.4237
>
> <SFU_2012_email_sig.jpg>
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--
Gerd Kortemeyer, Ph.D.
Associate Professor of Physics
Director, LON-CAPA Project
Michigan State University
http://www.msu.edu/user/kortemey/
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