Given are the following vectors: ā₁ āz a3 span{a1, 2, d3} span{a1, a2, a4, a5} span{a₂, a4} span{a2, a3, d4} span{a2, a3, a4, a5} span{a₁, d₂} span{a1, d2, a3, a4, a5} a4 ā5 = = = = = [−1,0,0] [-1,-1,0] [3,1, -2] [2,2,0] [3,-1,0] For which of the following subspaces of R³ does the orthogonal complement only consist of the zero vector?
Given are the following vectors: ā₁ āz a3 span{a1, 2, d3} span{a1, a2, a4, a5} span{a₂, a4} span{a2, a3, d4} span{a2, a3, a4, a5} span{a₁, d₂} span{a1, d2, a3, a4, a5} a4 ā5 = = = = = [−1,0,0] [-1,-1,0] [3,1, -2] [2,2,0] [3,-1,0] For which of the following subspaces of R³ does the orthogonal complement only consist of the zero vector?
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
![Given are the following vectors:
ā₁
āz
a3
span{a1, 2, 3}
span{a1, a2, 4, 5}
span{a₂, a4}
span{a2, a3, ã4}
span{a2, a3, a4, a5}
span{a1, a₂}
span{a1, a2, a3, a4, a5}
a4
ā5
=
=
=
=
=
[−1,0,0]
[−1,−1,0]
[3, 1, -2]
[2,2,0]
[3,-1,0]
For which of the following subspaces of R³ does the orthogonal complement only consist of the zero
vector?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b1c41e0-1a01-40ab-ae2e-a82ae6dd7ed0%2F8a7d9f7a-3f3c-47e9-8ec1-5c805264780b%2Fvjvinc_processed.png&w=3840&q=75)
Transcribed Image Text:Given are the following vectors:
ā₁
āz
a3
span{a1, 2, 3}
span{a1, a2, 4, 5}
span{a₂, a4}
span{a2, a3, ã4}
span{a2, a3, a4, a5}
span{a1, a₂}
span{a1, a2, a3, a4, a5}
a4
ā5
=
=
=
=
=
[−1,0,0]
[−1,−1,0]
[3, 1, -2]
[2,2,0]
[3,-1,0]
For which of the following subspaces of R³ does the orthogonal complement only consist of the zero
vector?
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