30. 0 0 0 0 0 2 3 2 4 3 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Use the method of Example 2.23 and Theorem 2.6 to determine if the sets of
by inspection (i.e., without calculation), state why. For any
sets that are linearly dependent, find a dependence relationship among the vectors.
The reference image of example 2.23 has been added
![Example 2.23
Determine whether the following sets of vectors are linearly independent:
Hand [1]
(b)
HD-
00-0
01-0
and
(a)
and
(d)
Solution In answering any question of this type, it is a good idea to see if you can
determine by inspection whether one vector is a linear combination of the others. A
little thought may save a lot of computation!
(a) The only way two vectors can be linearly dependent is if one is a multiple of
the other. (Why?) These two vectors are clearly not multiples, so they are linearly
independent.
(b) There is no obvious dependence relation here, so we try to find scalars 4₁, 4₂, 43
such that
1
8-8-8-8
The corresponding linear system is
q₁ +
G+q₂
and the augmented matrix is
C3 = 0
= 0
4₂ + c3 = 0
10 10
1 1
0 0
0 1
10.
=
Once again, we make the fundamental observation that the columns of the coefficient
matrix are just the vectors in question!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb82eee3-c597-43b7-b98f-cffc18fbca72%2F125855b3-2461-40ad-8b7e-efc3dea4e131%2Fcvn51n8_processed.png&w=3840&q=75)
Transcribed Image Text:Example 2.23
Determine whether the following sets of vectors are linearly independent:
Hand [1]
(b)
HD-
00-0
01-0
and
(a)
and
(d)
Solution In answering any question of this type, it is a good idea to see if you can
determine by inspection whether one vector is a linear combination of the others. A
little thought may save a lot of computation!
(a) The only way two vectors can be linearly dependent is if one is a multiple of
the other. (Why?) These two vectors are clearly not multiples, so they are linearly
independent.
(b) There is no obvious dependence relation here, so we try to find scalars 4₁, 4₂, 43
such that
1
8-8-8-8
The corresponding linear system is
q₁ +
G+q₂
and the augmented matrix is
C3 = 0
= 0
4₂ + c3 = 0
10 10
1 1
0 0
0 1
10.
=
Once again, we make the fundamental observation that the columns of the coefficient
matrix are just the vectors in question!
Transcribed Image Text:30.
0
0
• 0
0
2
>
0
3
2
4
3
2
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