Math 107 First Midterm Examination
October 3, 2008
NAME
(Please print)
Page
Score
2
3
4
5
6
Total
Instructions:
1. Do all computations on the examination paper.
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necessary.
2. Put answers inside the boxes (when applicable).
3. Please signify your adherence to the honor code:
I,
, have neither given nor received
aid in completion of this examination.
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Gaussian Elimination
(26 Points)
Score
1.
(20 points) Use Gaussian elimination to reduce
2
x
1
+ 3
x
2
+
x
3
= 4
x
1
+ 9
x
2

4
x
3
= 2
x
1

x
2
+ 2
x
3
= 3
to reduced rowechelon form.
I prefer that we never scale a row; in any case, we always
use a single row to create zeros in rows below it:
2
3
1
4
1
9

4
2
1

1
2
3
→
2
3
1
4
0
15
/
2

9
/
2
0
0

5
/
2
3
/
2
1
→
2
3
1
4
0
15
/
2

9
/
2
0
0
0
0
1
If you scale rows (as in the book’s form of Gaussian elimination), then you cannot use the
resulting row echelon form to compute a determinant.
2.
(6 points) Consider the following rowechelon tableau obtained by Gaussian elim
ination:
2
1
1
0
0

5

3
0
0
0
0
0
(a)
(2 points) Which unknowns in the linear system represented by this tableau
are free variables?
answer =
x
3
.
(b)
(2 points) Does the linear system have a solution?
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 Spring '07
 Trangenstein
 Math, Linear Algebra, Matrix Operations, Det, cj vj

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