3 -9 a = 2 b=-6 2 -6 For each of the following vectors, determine whether it can be written as a linear combination of these vectors. If so, give the linear combination using the vector names above. Select an answer > v₁ is not a linear combination v₁ is a linear combination: V1 = -1 -3 -27 V2=-18 -16 15 10 8 V3 = C= AŃ
3 -9 a = 2 b=-6 2 -6 For each of the following vectors, determine whether it can be written as a linear combination of these vectors. If so, give the linear combination using the vector names above. Select an answer > v₁ is not a linear combination v₁ is a linear combination: V1 = -1 -3 -27 V2=-18 -16 15 10 8 V3 = C= AŃ
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
![```plaintext
For each of the following vectors, determine whether it can be written as a linear combination of these vectors. If so, give the linear combination using the vector names above.
a = [ 3 b = [ -9 c = [ -3
2 -6 -2
2 ] -6 ] -1 ]
v₁ = [ -1
-1
-3 ]
<Select an answer>
<Select an answer>
v₁ is not a linear combination
v₁ is a linear combination:
v₂ = [ -27
-18
-16 ]
v₃ = [ 15
10
8 ]
<Select an answer>
```
This content is designed to help students understand how to determine if a given vector can be expressed as a linear combination of other vectors. The vectors `a`, `b`, and `c` are provided as a basis, and the task involves testing vectors `v₁`, `v₂`, and `v₃` against them. Students must decide if each `v` vector can be expressed as a combination of `a`, `b`, and `c`, and select their answers accordingly.
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80321e65-f5af-4407-990e-2a73bdb503ea%2F8336a61b-1788-4f84-b751-e1405a62f3f4%2F73md4hs_processed.png&w=3840&q=75)
Transcribed Image Text:```plaintext
For each of the following vectors, determine whether it can be written as a linear combination of these vectors. If so, give the linear combination using the vector names above.
a = [ 3 b = [ -9 c = [ -3
2 -6 -2
2 ] -6 ] -1 ]
v₁ = [ -1
-1
-3 ]
<Select an answer>
<Select an answer>
v₁ is not a linear combination
v₁ is a linear combination:
v₂ = [ -27
-18
-16 ]
v₃ = [ 15
10
8 ]
<Select an answer>
```
This content is designed to help students understand how to determine if a given vector can be expressed as a linear combination of other vectors. The vectors `a`, `b`, and `c` are provided as a basis, and the task involves testing vectors `v₁`, `v₂`, and `v₃` against them. Students must decide if each `v` vector can be expressed as a combination of `a`, `b`, and `c`, and select their answers accordingly.
```
Expert Solution
Step 1: To find.
In this question, we will write the vector as a linear combination of the given vectors.
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