Determine whether the following sets are subspaces of R³. Realize number 4 as the span of a collection of vectors. Justify your answers. 1. W₁ = = 2. W₂ = = 3. W3 = = a1 {}] a₂ € R³: a₁ = 3a2 and a3 = -A₂ -93) a1 a2 a3 a1 E a2 a3 € R³: : a₁ = a3 + 2 +9₁=0} E R³2a1 - 7a2 + a3
Determine whether the following sets are subspaces of R³. Realize number 4 as the span of a collection of vectors. Justify your answers. 1. W₁ = = 2. W₂ = = 3. W3 = = a1 {}] a₂ € R³: a₁ = 3a2 and a3 = -A₂ -93) a1 a2 a3 a1 E a2 a3 € R³: : a₁ = a3 + 2 +9₁=0} E R³2a1 - 7a2 + a3
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
![Determine whether the following sets are subspaces of R³. Realize number 4
as the span of a collection of vectors. Justify your answers.
1. W₁
2. W₂
3. W3
4. W₁
5. W5
6. W6
=
=
=
=
a1
{]
a3
=
a2 € R³ : a₁ = 3a2 and a3 = -a₂
a}
a1
a2
a3
a1
{E
a2
a3
€ R³: a₁ = a3 + 2
a1
{B]
a2
az
a1
B
a2
аз
ER³2a1 - 7a₂ + a3 =
€ R³: a₁
+0=0}
a1
{B]
a2
a3
4a2-a3 =
€ R³: a₁ + 2a2 - 3a3
-₁}
€ R³ : 5a² − 3a² + 6a² = 0
Ba² = 0}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7538180c-5348-4d54-a5c1-c840ed6fc5b5%2F6febe297-26a9-4ae8-8c42-bad5454fda01%2F47bz13_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine whether the following sets are subspaces of R³. Realize number 4
as the span of a collection of vectors. Justify your answers.
1. W₁
2. W₂
3. W3
4. W₁
5. W5
6. W6
=
=
=
=
a1
{]
a3
=
a2 € R³ : a₁ = 3a2 and a3 = -a₂
a}
a1
a2
a3
a1
{E
a2
a3
€ R³: a₁ = a3 + 2
a1
{B]
a2
az
a1
B
a2
аз
ER³2a1 - 7a₂ + a3 =
€ R³: a₁
+0=0}
a1
{B]
a2
a3
4a2-a3 =
€ R³: a₁ + 2a2 - 3a3
-₁}
€ R³ : 5a² − 3a² + 6a² = 0
Ba² = 0}
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
