# Using linearTransformation (Shock Wave)

Click here to open a new window with this Shock Wave Lite Applet. Resize the new window and arrange your desktop so you can move-back-and-forth between these two windows.

The new window 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 Shock Wave Lite Applet 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.

• The vector x is represented visually by a small blue sphere. Its components are displayed numerically in the right hand panel.

• The vector y is represented visually by a slightly larger reddish-brown sphere and its components are also displayed numerically in the right hand panel. Notice as you drag the vector x the vector y moves accordingly and the numeric displays are updated.

• The entries in the matrix A are displayed numerically in the right hand panel. These entries may be edited in the usual way. Notice that, as you edit the entries in the matrix A, the vector y is immediately adjusted.

• 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.

You can specify various elements of the display using the parameters described below.

Parameters

• sw1 -- This parameter determines whether or not the matrix A appears on the screen. Most often it should appear on the screen, so that users can see the connection between the entries in the matrix and the behavior of the linear transformation it represents. There are, however, times when this matrix should not appear -- for example, if students are asked to determine the matrix from the behavior of the linear transformation. If the value of the parameter sw1 is hideA the matrix will be hidden. Otherwise it will be displayed.

• sw2 -- This parameter determines whether the vector b is shown. When this lite interactive component is being used to study linear equations of the form Ax = b this vector is usually shown. When it is used to study linear transformations of the form y = Ax then ths vector is usually not shown. If the value of sw2 is hideB the vector will be hidden. Otherwise it will be displayed.

• sw3 -- This parameter specifies the initial entries in the matrix A. This parameter has the form [a11, a12, a21, a22]. For example, reflection through the origin is represented by [-1, 0, 0, -1]. Notice that if the matrix A is displayed the user can change its entries by editing the displayed entries.

• sw4 -- This parameter specifies the initial value of the vector x in the form [x1, x2]. Notice that the user can change the vector x by dragging the blue dot representing it.

• sw5 -- This parameter specifies the initial value of the vector b in the form [b1, b2]. Notice that if the vector b is displayed the user can change its value by editing its entries.

Part of the code calling this lite interactive component is shown below. Notice that the parameters must be entered twice in different forms. Each form is recognized by some but not all browsers. The relevant code is highlighted in red and in blue. Be careful to enter the parameters as shown. We recommend that you copy the code from one of the examples below and edit the appropriate entries. Examples: