Linear Systems
(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
x
1
+ 2
x
2

2
x
3
+
x
4
=
2
2
x
1

x
2
+
x
3
+ 7
x
4
=

1

3
x
1
+
x
3
+
x
4
=
1
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
2
(7) Solve the linear system using GaussJordan method:
x
1
+ 2
x
2
+ 3
x
3

x
4
=
3
2
x
1
+ 3
x
2
+
x
3
=
9
3
x
1
+ 5
x
2
+ 2
x
3

3
x
4
=
10
(8) Find conditions on
k
and
l
so that the system
x
+
y
+ 2
z
=
4
2
x
+ 3
y

z
=
4
3
x
+ 4
y

kz
=
l
has
(a) unique solution
(b) infinitely many solutions
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 MS.SIMPSON
 Linear Systems, Englishlanguage films, 2k, infinitely many solutions

Click to edit the document details