Follow the directions of Exercise 21 for the linear system in Example 6 of Section 1.2. 21. For the linear system in Example 5 of Section 1.2, express the general solution that we obtained in that example as a linear combination of column vectors that contain only numerical entries. [ Suggestion : Rewrite the general solution as a single column vector, then write that column vector as a sum of column vectors each of which contains at most one parameter, and then factor out the parameters.] EXAMPLE 6 | A Homogeneous System Use Gauss–Jordan elimination to solve the homogeneous linear system x 1 + 3 x 2 − 2 x 3 + 2 x 5 = 0 2 x 1 + 6 x 2 − 5 x 3 − 2 x 4 + 4 x 5 − 3 x 6 = 0 5 x 3 + 10 x 4 + 15 x 6 = 0 2 x 1 + 6 x 2 + 8 x 4 + 4 x 5 + 18 x 6 = 0 (4)
Follow the directions of Exercise 21 for the linear system in Example 6 of Section 1.2. 21. For the linear system in Example 5 of Section 1.2, express the general solution that we obtained in that example as a linear combination of column vectors that contain only numerical entries. [ Suggestion : Rewrite the general solution as a single column vector, then write that column vector as a sum of column vectors each of which contains at most one parameter, and then factor out the parameters.] EXAMPLE 6 | A Homogeneous System Use Gauss–Jordan elimination to solve the homogeneous linear system x 1 + 3 x 2 − 2 x 3 + 2 x 5 = 0 2 x 1 + 6 x 2 − 5 x 3 − 2 x 4 + 4 x 5 − 3 x 6 = 0 5 x 3 + 10 x 4 + 15 x 6 = 0 2 x 1 + 6 x 2 + 8 x 4 + 4 x 5 + 18 x 6 = 0 (4)
Follow the directions of Exercise 21 for the linear system in Example 6 of Section 1.2.
21. For the linear system in Example 5 of Section 1.2, express the general solution that we obtained in that example as a linear combination of column vectors that contain only numerical entries. [Suggestion: Rewrite the general solution as a single column vector, then write that column vector as a sum of column vectors each of which contains at most one parameter, and then factor out the parameters.]
EXAMPLE 6 | A Homogeneous System
Use Gauss–Jordan elimination to solve the homogeneous linear system
x
1
+
3
x
2
−
2
x
3
+
2
x
5
=
0
2
x
1
+
6
x
2
−
5
x
3
−
2
x
4
+
4
x
5
−
3
x
6
=
0
5
x
3
+
10
x
4
+
15
x
6
=
0
2
x
1
+
6
x
2
+
8
x
4
+
4
x
5
+
18
x
6
=
0
(4)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
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