Rational Matrix Workbench
This Mathwright Web activity supports easy definition and manipulation of matrices. The screen layout (below)
features three windows: Enter commands in the bright yellow
command window, see results in the pale yellow display window, and read instructions in the white help window. New matrices (initialized to 0) are created in the display window at the touch of a button. These are edited word processor style, and the end result is then assigned to any variable name with another button.At the top of the screen are quick links to instructions for the available commands, as shown below:
Here is a description of most of the commands:
pr
The pr command is for printing matrices in the pale yellow window.show The command to print a numerical or symbolic result in the pale yellow window
tr The transpose operation
row Extracts one row from a matrix
col Extracts one column from a matrix
augment Combines two matrices side by side into a single augmented matrix
rref Computes the reduced row echelon form for a matrix
cmat Creates a constant matrix with specified dimensions
diag Creates a diagonal matrix with specified vector of diagonal entries
det computes the determinant of a square matrix
inv Determines the exact rational inverse of a square matrix
circ Creates a circulant matrix with specified entries in the first row
cpoly Determines the characteristic polynomial of a square matrix
kronecker creates the kronecker product of two matrices
Sample Activity: Explore how the columns of a matrix are related to the columns of its reduced row echelon form.
It is easy to get confused about the significance of the rows and columns of the reduced echelon form. In particular, the idea that both matrices have the same dependencies among columns can cause confusion for students. Using this interactive webpage, students can enter a matrix A, then compute the reduced echelon form. Next, have them determine dependencies among the columns of the reduced form by inspection (requires them to think about it!). So, for example, perhaps they observe that the third column is 2 times the first plus 3 times the second. Now in the original matrix A, they can compute this same combination by entering the command
pr 2*col(1,A) + 3*col(2,A)
Then visually confirm that that is the same as column 3 of A. This combination of instant machine computation with required thinking about relationships among the parts can make a powerful pedagogical impact.
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.