Math 118

Chapter 6

Practice test

You have a 35 point test on Tuesday, October 30.  It will look a lot like this:

            No calculators.  You should be able to do this whole test using numbers no bigger than 20.  You don’t need a calculator for that.

            Show your work.  Show your matrix at each step, and tell what you do to get to the next step.

1.         5 points            Write find the “augmented matrix” corresponding to the following linear system:

                        2x        +y         + z       = 9

                        3x        + y       + z       = 12

                        2x         -y         + z       = 5 

2.         (20 points) Use Gauss-Jordan elimination to put this matrix into reduced row echelon form.  Show your steps, and, for each step, use the notation in the book (something like “R₂ + 2* R₁” or “3*R₃”) to tell what you did at each step.  Do the work on the back of this page, and write the final form in the space below:

3.         (5 points)          What does your reduced row echelon form tell you that the solution to the system of equations is?

x = _____                    y = _____                    z = _____

4.         (5 points)          Show how to check your solution to make sure it is correct (or, if your solution is incorrect, how the check shows it is incorrect).

To find the answers, look at the December line of the calendar on the course home page.