Math 118

Chapter 6

Practice test

You have a 35 point test on Thursday, March 13.  It will look a lot like this:

            No graphing calculators or cell phones. 

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

3.        (5 points)    Write the equations that are equivalent to your matrix in row echelon form.

4.        (5 points)    Solve those equations in the most efficient way, and find the solutions to the original system of equations.

x = _____                    y = _____                    z = _____

5.         (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 April line of the calendar on the course home page.