Row Reduction

by Dan Kalman

This Mathwright Web activity allows students to apply a sequence of row operations to a matrix. The student specifies each row operation descriptively, and observes the results. See the screen shot below.

Observe that in the pale yellow *output window*, the row operations and their results are both displayed. To illustrate how the interaction proceeds, here is a description of the three steps that led to the screen above. First, on the part of the screen that looks like this --

-- the student enters 1 in the first yellow box and 2 in the second, and clicks on the word GO! to interchange the first two rows of the matrix. The output window displays the result:

Next, using this input line --

-- the student again fills in the yellow blanks to define a desired operation, entering a -2 in the first blank, a 1 in the second, and a 2 in the third. Clicking the word GO! again produces the next section of the output window.

The next step is to eliminate the first 2 in row 3. This is accomplished similarly, by changing the third yellow box in the input line above to indicate row 3 instead of row 2.

As the student continues to perform row operations, a record is generated in the output window showing each operation performed, and the successive results.

The operations that may be invoked are interchanging two rows, multiplying a row by a scalar, and adding a multiple of one row to another. It is possible to begin with any matrix the user cares to enter, or to generate a random matrix. There is also a link which adjoins an identity matrix to the right of the given matrix. The activity opens up in *exact fraction mode* -- meaning that all operations are performed in exact arithmetic using fractions. However, the user can switch to *decimal mode*, which employs floating point arithmetic. In this mode, the user also specifies the number of decimal digits to be displayed in the output window.

Sample Classroom Activities: Begin with an identity matrix and apply various row operations to observe the creation of elementary row matrices; Execute a row operation, and then find a way to undo that operation and restore the original matrix.

If you have already installed the Mathwrightweb plug-in for Internet Explorer, you can try this activity by clicking TRY IT NOW. If you need instructions for obtaining the plug-in, or more information about Mathwright activities and software, click on GET MORE INFO. You can also click on GO TO DAN KALMAN'S MATHWRIGHTWEB ACTIVITY LIST.