# Math 3323 Matrix Algebra Investigation 1

## Dr. Duval

Open this Mathematica page in a new browser window, so you can see both these instructions and the Mathematica grapher at the same time.

### The First two systems

1. x + 6y - 8z = 0
4x + y - z = 0
4x + y - 10z = 0
2. 3 + 10x = z
1 + x = z
3 - 8x = z

### Experiments

1. Enter the equations in part i. into the boxes to the right, and run each of the box by pushing "plot functions" button. Since each equation already has 0 on one side of the equation, you just have to enter the non-zero side of each equation into each box.
2. Answer the following questions:
1. Based on the graph, make an educated guess on the solution set for the system. Now, solve the system algebraically.
2. Compare the two solution sets obtain in part a.
3. Now, enter the linear system given in part ii into the Mathematica Commands. This time, since the equations do not have 0's on either side of the equation, you'll need to rewrite each equation so that there is a 0 on one side, and then put the non-zero side of each equation into each box.

And next, answer the questions given in the second step (questions in parts 2a and 2b) for the system given in part ii.

4. Enter your own set of examples of linear and nonlinear systems of equations, and experiment on them. As a result of your experimentation, conjecture on all the types of solutions system of linear equations can have.

### Report

Write a summary of your observations and conjectures. Describe all the experiments that you did. List all the conjectures you made (including any that later turned out to be false), how you came up with them, how you tested them, and which ones you still think are true. Please use clear, complete sentences, and organize your report.