306 The Matrix Morphing Game
When you get the unit diagonal form, you should end up with sloppy fractions in the far-right column.
When you reduce these fractions, you should get
1002
010 − 1
0013
Solution
You’re on your own. Have fun!
Practice Exercises
This is an open-book quiz. You may (and should) refer to the text as you solve these problems.
Don’t hurry! You’ll find worked-out answers in App. B. The solutions in the appendix may not
represent the only way a problem can be figured out. If you think you can solve a particular
problem in a quicker or better way than you see there, by all means try it!
- Put the following three-by-three linear system into the proper form for conversion to
matrix notation:
x=y−z− 7
y= 2 x+ 2 z+ 2
z= 3 x− 5 y+ 4 - Write the set of equations from the solution to Prob. 1 in the form of a matrix.
- Write the set of equations represented by the following matrix:
(^04) − 1 − 2
(^5) −3/2 81
1111
- Put the matrix of Prob. 3 into echelon form.
- Put the matrix derived in the solution to Prob. 4 into diagonal form.
- Reduce the matrix derived in the solution to Prob. 5 to a form with the smallest possible
absolute values in each row, such that all the numbers in the matrix are integers. - Reduce the matrix derived in the solution to Prob. 6 to unit diagonal form. Then state
the tentative solution to the three-by-three linear system we derived from the matrix in
Prob. 3 and stated in solution 3. - Check the values for x,y, and z derived in the solution to Prob. 7 to be sure they’re
correct. To do this, plug the numbers into the equations stated in the solution to Prob. 3.