# Interactive Online Modules for Matrix Algebra and Linear Algebra

## Linear Systems

#### Linear Systems Module (Java)

#### Sample Investigation:

Equivalent Systems and solution sets

#### Other Topics that Can Be Covered Using this Module:

- Equivalent Systems
- Elementary Operations
- Consistent and Inconsistent Systems
- Trivial and Nontrivial Solutions

#### Module Description

This module was developed using Geometer's SketchPad (GSP).

In the context of two linear equations with two unknowns, this module is designed to illustrate the geometric representations of linear equations.

The option "Hide Points" should be chosen first. Next, consider the system of equations (and their graphs), for example:

*2x-y=-2*

*-4x-y=-8*

The graphs of the linear equations in the
system are two blue lines (in the initial stage one blue line coincides with
a red line; sliding *k* makes the two blue lines visible).
The first equation is multiplied by a constant *k* (initially *k=0*), and then added to the second equation.
The resulting equation's graph is a red line. The objective is to choose a value
for *k* so that the resulting red line becomes horizontal or vertical.
Then you can read its *y-* or *x-* intercepts.
For those values of *k* the resulting
equation can be put in a form having one of the coefficients equal 0.

The option "Show Points" should be chosen and two pairs of points defining two equations of a system and their corresponding blue lines are displayed. New systems of equations can be created dragging the two red points on each blue line.

The "Reset" button returns the system to the initial settings.

The "Show/Hide Grid" button allows to read the values of *k*
and the solution of the system more accurately.