The vectors listed in Eq. (10) are used in several of the exercises that follow. VI = [2]· 2 -[3]. »-[2]· V3 V2 = 3 --[B]-~-B] = [³] · 6 u= u₁ U₂ = 0 --[:]· []-[] [] (3) u3 U4 -[]---[] 0 0 (10) In Exercises 1-14, use Eq. (6) to determine whether the given set of vectors is linearly independent or linearly dependent. If the set is linearly dependent, express one vector in the set as a linear combination of the others. 1. {V₁, V₂} 2. {V1, V3} 3. {V1, Vs) 4. (V2, V3)
The vectors listed in Eq. (10) are used in several of the exercises that follow. VI = [2]· 2 -[3]. »-[2]· V3 V2 = 3 --[B]-~-B] = [³] · 6 u= u₁ U₂ = 0 --[:]· []-[] [] (3) u3 U4 -[]---[] 0 0 (10) In Exercises 1-14, use Eq. (6) to determine whether the given set of vectors is linearly independent or linearly dependent. If the set is linearly dependent, express one vector in the set as a linear combination of the others. 1. {V₁, V₂} 2. {V1, V3} 3. {V1, Vs) 4. (V2, V3)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![The vectors listed in Eq. (10) are used in several of the
exercises that follow.
V₁ =
·-[2]· » -[3]· »»-[²]·
V2
V3 =
--8--8
V4=
-0-0-0
=
=
=
-0-0-0
=
3
1. {V1, V₂}
3. {V₁, Vs}
=
(10)
In Exercises 1-14, use Eq. (6) to determine whether the
given set of vectors is linearly independent or linearly
dependent. If the set is linearly dependent, express one
vector in the set as a linear combination of the others.
2. (V1, V3)
4. (V2, V3}
5. {V1, V2, V3)
7. {u4, us}
9. {u1, U₂, us}
11. (u₂, U4, us)
13. {uo, u₁, U2, U4}
15. Consider
ing Th
6. (V2, V3, V4}
8. (U3, U4)
10. {u₁, U4, us}
12. (u₁, U₂, U4)
14. (uo, U2, U3, U4}
ITs-
(11)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F624dcfab-19f1-4c4b-b3ec-94b9a5b18d08%2F4e4cf4ed-4ed4-437a-82e0-845271e4ea13%2Fo553h06_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The vectors listed in Eq. (10) are used in several of the
exercises that follow.
V₁ =
·-[2]· » -[3]· »»-[²]·
V2
V3 =
--8--8
V4=
-0-0-0
=
=
=
-0-0-0
=
3
1. {V1, V₂}
3. {V₁, Vs}
=
(10)
In Exercises 1-14, use Eq. (6) to determine whether the
given set of vectors is linearly independent or linearly
dependent. If the set is linearly dependent, express one
vector in the set as a linear combination of the others.
2. (V1, V3)
4. (V2, V3}
5. {V1, V2, V3)
7. {u4, us}
9. {u1, U₂, us}
11. (u₂, U4, us)
13. {uo, u₁, U2, U4}
15. Consider
ing Th
6. (V2, V3, V4}
8. (U3, U4)
10. {u₁, U4, us}
12. (u₁, U₂, U4)
14. (uo, U2, U3, U4}
ITs-
(11)
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