The site contains a JavaScript applet for solving systems of linear equations together with a page of notes describing the link between solving systems of linear equations and inverting a matrix. The applet can handle systems of up to 10 equations, and solutions are given to 3 decimal places. This page is part of a larger site on the relations between solving equations, matrix inversion and linear programming, which can be found at http://ubmail.ubalt.edu/~harsham/opre640a/partXII.htm.

Also of interest may be the reviews of these similar items:

Any web browser capable of reading Javascript (i.e. any web browser)

Technical Requirements:

The site is primarily designed to solve systems of linear equations. With careful guidance, students could use this ability to make and verify conjectures about the solvability or non-solvability of systems depending on the coefficient matrix, or to compute inverses of matrices.

Identify Major Learning Goals:

The stated goal of the site is to extend ?the existing one-way connections among the solving linear systems of equations, matrix inversion, and linear programming?. The page under review is concerned with the first two of these topics.

Target Student Population:

Linear Algebra students or anyone who needs to solve linear systems.

Prerequisite Knowledge or Skills:

Basic knowledge of systems of linear equations.

Content Quality

Rating:

Strengths:

The applet is reasonably straightforward and intuitive: the user enters the coefficients and right-hand sides of the equations into a preset 10 by 11 array; if fewer than 10 equations are needed, the coefficients are to be placed in the top left corner of the array, with the remaining entries left at their default value of 0. There is a ?Calculate? button to produce the solutions, and a ?Reset? button to return all entries to the default value.

The page of notes and examples also serves nicely as a set of instructions for the applet.

Concerns:

The notes could be clearer in places, and there are some errors: the alleged solution to Numerical Example 1 is incorrect, and there are several places in Numerical Example 2 where X1 should be replaced by X2.

The 10-equation, 3-decimal-place limit of the applet limits its use for serious work, though they are fine for its original purpose as a classroom or teaching tool.

A more subtle concern is that the user is required to enter equations with a non-zero coefficient for X1 first. This may require re-ordering the equations, which in turn could obscure the relation between solving and inverting. (Could a student come to the conclusion that a matrix with entry 0 in the first row and column cannot be invertible, for example?) Perhaps the applet could be rewritten so that this re-ordering of the equations was done internally.

It would be nice if the applet could distinguish between the ?error message? cases with no solutions and infinitely many solutions.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

The applet efficiently carries out a computation which would be hard to do by hand. As mentioned above, it could lend itself to experimentation and conjecture on the existence and behavior of solutions of linear systems,
and possibly matrix inverses.

A nice feature is that the coefficient array is not cleared when the solution is calculated. This makes it easy to solve several systems with the same coefficient matrix but different right-hand sides. (This is what is needed, of course, to show the relation between solving the equations and inverting the coefficient matrix.)

The applet can be used as an aid to a lecture or as a quick in-class demonstration.

Concerns:

Classroom activities with larger systems may be slowed down by the time needed to enter the original matrix term-by-term. (This is probably unavoidable in matrix computations, though.)

Ease of Use for Both Students and Faculty

Rating:

Strengths:

The applet is very easy to use. The average user can begin using the applet immediately.

Concerns:

The possible need to re-order equations, so that equations with a non-zero coefficient for X1 appear first, may be confusing to an inexperienced user even though it is explained in the notes.

The site could use a better Web design. For example, numerical examples can be hyperlinked to a separate page so the user would not have to scroll down that much to get to the applet.

Creative Commons:

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