We present three interactive web-based demonstrations which help teach students the basics of addition, subtraction, and multiplication on matrices. In virtue of their instant feedback and self-paced nature, they are ideal learning tools for anyone who wishes to learn the concepts involved through directed practice. We recommend them especially strongly for use with non-majors, or for courses with a primary focus other than mathematics.
Matrix Addition and Subtraction
This program allows the user to choose the dimensions of the matrices to be operated upon, and input integer values for each cell. The user then chooses to add or subtract the matrices, and the program automatically displays the result. By comparing the final values with those in the intial matrices, the user is able to see the effects of matrix addition and subtraction in as many concrete examples as s/he desires.
Stepwise Matrix Multiplication
Because multiplication for matrices is significantly more complex than addition/subtraction, this demonstration uses a particular example to show the user every step in the process separately, and does not progress to the next step until the user opts to do so. By using visual cues to highlight the significant portions of the input, the program manages the user's attention in a helpful manner.
To test the user's understanding of the processes demonstrated in the previous program, this one allows the user to enter matrix dimensions and values, but then requires the user to perform the calculation. If the user errs, the erroneous entries in the final matrix are highlighted by the program, which then recommends that the user try those cells again. The user may continue to use this practice tool to get immediate feedback on her/his performance until mastery is achieved.