MTH 119 — Spring — 2005
Essex County College — Division of Mathematics
Quiz # 11— January 18, 2005
Name:
Signature:
Show all work clearly and in order, and box your final answers. Justify your answers algebraically
whenever possible. You have 20 minutes to take this 10 point quiz. When you do use your
calculator, sketch all relevant graphs and write down all relevant mathematics.
1. Solve by using elementary row operations.
2x+ 3y+z=−1
3x+ 3y+z= 1
2x+ 4y+z=−2
Augmented matrix form of the system:
2 3 1 −1
3 3 1 1
2 4 1 −2
Elementary row operations, in order given:
−3R1+ 2R2→R2
−1R1+R3→R3
Produces:
231−1
3 3 1 1
241−2
∼
231−1
0−3−1 5
010−1
The last row gives y=−1 ; using y=−1 in row two, gives z=−2 ; finally, using y=−1
and z=−2 in row one, gives x= 2 .
1This document was prepared by Ron Bannon using L
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