Using linearTransformation or linearSystem

Click here to open a new window with a form that enables you to create your own Web page using the osslet linearTransformation. Resize the new window and arrange your desktop so you can move-back-and-forth between these two windows. Creating a web page requires three steps.

1. Using the form that you just opened you create the html code that configures the osslet the way that you want it configured. You do not need to know any programming.
   
   
2. Copying the code created by this form into your own Web page. You can use your favorite Web page editor -- for example, Microsoft Front Page.
   
   
3. Downloading the file linearTransformation.dcr and placing it in the same directory as any html pages that use this osslet. To download a file option-click the link in MacOS or right-click and choose the appropriate option in Windows.

As you fill out the form to configure the osslet for your own use, you may want to refer to this example, which shows all the possible elements in the linearTransformations display. As a curriculum developer you can choose to omit some of these elements to simplify the display. This osslet enables users to study two dimensional linear transformations of the form y = Ax or systems of two equations in two unknowns of the form Ax = b visually.

1. First enter a title to appear in your new web page. When you test your work the new web page will open in a new window with this title.
   
   
2. The entries in the matrix A are displayed numerically in the right hand panel. These entries may be edited in the osslet by the user in the usual way. You specify the initial entries for this matrix in the next block of entries in the form. This block also has a check box that lets you specify whether the matrix is shown on your Web page. If, for example, you were creating Web pages with questions asking students to determine the matrix based on the behavior of the linear transformation, you would not want the matrix to be visible.
   
   
3. The vector x is represented visually by a small blue sphere. Its components are displayed numerically in the right hand panel. The next entries enable you to specify the initial vector x. The user can change this vector by dragging the blue sphere.
   
   
4. The vector b is represented visually by a black square and its components are displayed numerically in the right hand panel. They may be edited in the usual way. The next group of entries enables you to specify the initial vector b. A check box enables you to specify whether the vector b is displayed or not. You probably will want this vector displayed when you are using this osslet for units involving a system of equations or for units exploring the range of a linear transformation. You probably will not want this vector displayed in many other units.

After you have filled out the form click the Try it!! button to test what you've done. You can make changes in the form and then click the Try it!! button again.

When you are satisfied with the results, choose View Source in your browser. You should see something like the figure below. Its exact appearance will depend on your browser and the choices you made as you filled out the form. The figure only shows the left part of the source code because the source code is very wide.

Locate the part of the code between the line that begins <!-- Copy the code below and the line that begins <!-- Copy the code above. Highlight this code; copy it; and paste it into the (html view of) page you are creating. After you've pasted this code into your new page you can edit your new page in your usual way. Note depending on the software you use to create Web pages, the osslet may not appear until you look at it in a browser. For example, in Microsoft Front Page the osslet does not appear even in the preview pane. It only appears when you look at the page in a browser.

The steps for making a web page with the linearSystem variation of this osslet are almost identical except that you use this form and you need to download the file linearSystem.dcr and place it in the same directory as your html page. The linearSystem form does not give you the option to display the vector b since there is no need for this vector when you are working with a linear system of differential equations.