Practice Problems
MTH 2201
3/20/2008
1. Suppose that the augmented matrix for a system of linear equations has been
reduced by row operations to the given reduced row echelon form. Solve the
system. Assume that the variables are named
x
1
, x
2
, ...,
from left to right.
(
i
)
1 0 0

3
0 1 0
0
0 0 1
7
(
ii
)
1 0 0

7
8
0 1 0
3
2
0 0 1
1

5
(
iii
)
h
1 2 0 2

1 3
i
2. Suppose that the augmented matrix for a system of linear equations has been
reduced by row operations to the given row echelon form. Solve the system by
reducing the matrix to reduced row echelon form. Assume that the variables
are named
x
1
, x
2
, ...,
from left to right.
(
i
)
1

3 4 7
0
1 1 2
0
0 1 5
(
ii
)
1 7

2 0

8

3
0 0
1 1
6
5
0 0
0 1
3
9
0 0
0 0
0
0
3. Solve the linear system by Gauss Jordan elimination:
(i)
x
1
+
x
2
+2
x
3
= 8

x
1

2
x
2
+3
x
3
= 1
3
x
1

7
x
2
+4
x
3
= 10
(ii)
3
x
1
+ 2
x
2

x
3
=

15
5
x
1
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 Spring '08
 Kigaradze
 Linear Equations, Equations, Row echelon form

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