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(1) Use the GaussJordan method to solve:
x
1

x
2
+
x
3
+ 2
x
4
= 7
2
x
1

x
2
+ 3
x
4
= 12

x
1
+
x
2
+
x
3

2
x
4
=

7
(2) Given the linear system

x
1
+
x
2

x
3

2
x
4
= 0
5
x
1

3
x
2
+
x
3
+ 4
x
4
= 2
8
x
1
+ 3
x
2

15
x
3

15
x
4
= 8
(a) Find the general solution by using GaussJordan elimination.
(b) Find the particular solution for which
x
1
= 7.
(3)
2
x
1

3
x
2
+
x
3
= 7
x
1

2
x
2

x
3
+
x
4
= 2
3
x
1

5
x
2

x
3
+ 2
x
4
= 9
(a) Find all solutions of the given system.
(b) If the system has more than one solution, ﬁnd a particular solution.
(c) Can you use Cramer’s rule to solve this system? Explain.
(4) Solve the following linear system. If there is more than one solution give a
particular solution.
2
x
1

3
x
2
+
x
3
= 6
2
x
1

2
x
2

x
3
+ 3
x
4
= 1
3
x
1

5
x
2

x
3
+ 2
x
4
= 8
(5) Find the general solution to the homogeneous linear system:
x
1
+ 3
x
2

4
x
3
+ 2
x
4
= 0
2
x
1
+ 7
x
2

6
x
3
= 0

3
x
1

8
x
2
+ 14
x
3

10
x
4
= 0
(6) Solve by using the GaussJordan elimination
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This note was uploaded on 10/03/2010 for the course PHYS. 203NYA05 taught by Professor Ms.simpson during the Fall '09 term at Dawson College.
 Fall '09
 MS.SIMPSON

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