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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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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}
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}
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