MaplePrimes - answers and comments on Question, Advanced Linear Algebra Questions

Matrix

acer — Tue, 09 Feb 2010 03:13:55 Z

I may be in the minority here, but I prefer using the Matrix() constructor with its listlist argument for the data. For example, I find that I only very rarely get the syntax wrong for something like this,

Matrix([[1,3],[-3,1]]);

You might also consider guessing what the common syntax mistakes are with using the angle brackets, and perhaps even convert/accept typical mistakes. For example, you could convert, <<1,3>,<3,-1>> and give partial or full marks.

acer

I see your point. Getting

mjmoore — Tue, 09 Feb 2010 20:55:54 Z

I see your point. Getting the student to actually construct a matrix with the Matrix command would be easier for someone just learning to use Maple and not aware of the angle bracket notation. What I was trying to get at was that even with the Matrix(); command, at least 1 in 10 people are going to mess up with the syntax - an extra comma accidentally, or one missing bracket - and with the large number of students taking this course in the future, we run the risk of having a lot of remarking to do.

My goal is to get a format that the students can easily enter their answer into once they've done the 'on paper' work. Ideally they shouldn't have to enter a bunch of Maple syntax. For example I created a template with 16 response areas arranged in the shape of a matrix. This works for things like inverses when there is only one corresponding answer, but for something like diagonalization where the order of the vectors can be random and scalar multiples of those vectors are also valid answers, I can't do something like that.

Mike

agree

longrob — Tue, 09 Feb 2010 11:04:23 Z

I agree with acer here. As a new student of Maple I find that using angle brackets is prone to error, but using square brackets is quite intuitive, even for a 4x4 matrix.

TA allows for more flexibility

Doug Meade — Tue, 09 Feb 2010 22:17:13 Z

Your array of 16 response areas is probably the way to go, but I think you are unnecessarily limiting the types of problems for which this could be used.

If I were doing this, I would write code to collect the user's information from these cells as a matrix, and then use the relevant mathematics to check if this matrix is correct. Using your example of a diagonalizing matrix, this would involve multiplying the student's answer and the original matrix and checking that the result is diagonal.

Here's a simple implementatin of a test if a matrix is diagonal:

IsDiagonal := A -> ArrayTools:-IsZero( A - LinearAlgebra:-DiagonalMatrix( LinearAlgebra:-Diagonal( A ) ) );

Lastly, I would suggest that you might create a general array with, say, 36 response areas and have the instructions emphasize that students should fill in only those entries for the appropriate size of the response. (You could have two extra fields for the number of rows and columns, but I prefer the idea of having some areas left empty and modifying my answer checker to check that the student's answer has the correct shape and size.

Just a couple of thoughts that I hope are of some use,

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

Collecting answers?

mjmoore — Tue, 09 Feb 2010 23:05:23 Z

I had the same idea Doug, but I can't see how to implement it.

You said that you would write a code to collect the users information from all 16 seperate response areas, and then convert that to a matrix and use maple grading code to determine its correctness. Do you know of a way to do this? The IsDiagonal code you supplied would work for grading, but it's the data collection process that I'm struggling with.

I suppose my question now becomes is it possible for Maple TA to pass a users answer from one response area to another? It would also be interesting to know if it is possible to store a users response as a temporary variable that can be accessed in the grading code of another.

Thanks,
Mike

multiple response in a single TA question: possible or not?

Doug Meade — Wed, 10 Feb 2010 01:51:28 Z

I have to admit that I am not, currently, a MapleTA user. I thought it was possible to have multiple response fields in a single question, but as I look over the documentation it appears my memory is faulty. Maybe you can do something with a multipart question, but I did not see anything explicit showing how this might be done.

Hopefully, someone else with more current working knowledge of MapleTA, and it's possibilities, will be able to point you in a good direction.

Doug

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Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu