3. Consider these vectors in R²: V₁ = -[4] (a) Find coefficients to express the vector 3 V2 - H 3 as a linear combination of v₁ and v2. (b) Given an arbitrary vector T [3] show that it can be written as a linear combination of v₁ and v2. (Find formulas for the coefficients a and az in terms of x and 20 y.) (c) Describe span {V1, V2} within R2 using words and pictures. (d) Are the vectors (V1, V2} linearly independent? Justify your answer. (e) Is the matrix V1 V2 invertible? If so, find its inverse. How is this connected to your work above? Vi
3. Consider these vectors in R²: V₁ = -[4] (a) Find coefficients to express the vector 3 V2 - H 3 as a linear combination of v₁ and v2. (b) Given an arbitrary vector T [3] show that it can be written as a linear combination of v₁ and v2. (Find formulas for the coefficients a and az in terms of x and 20 y.) (c) Describe span {V1, V2} within R2 using words and pictures. (d) Are the vectors (V1, V2} linearly independent? Justify your answer. (e) Is the matrix V1 V2 invertible? If so, find its inverse. How is this connected to your work above? Vi
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 13CR
Related questions
Question
![3. Consider these vectors in R²:
V₁ =
-[4]
(a) Find coefficients to express the vector
3
V2
- H
3
as a linear combination of v₁ and v2.
(b) Given an arbitrary vector
T
[3]
show that it can be written as a linear combination of v₁ and v2.
(Find formulas for the coefficients a and az in terms of x and
20
y.)
(c) Describe span {V1, V2} within R2 using words and pictures.
(d) Are the vectors (V1, V2} linearly independent? Justify your answer.
(e) Is the matrix V1 V2 invertible? If so, find its inverse. How is this connected to your work above?
Vi](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf909276-6ad3-4144-b98c-235c5a32e436%2Fe3806ccd-dd3d-4c56-8077-f83f749dbe6e%2F6e04d0q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider these vectors in R²:
V₁ =
-[4]
(a) Find coefficients to express the vector
3
V2
- H
3
as a linear combination of v₁ and v2.
(b) Given an arbitrary vector
T
[3]
show that it can be written as a linear combination of v₁ and v2.
(Find formulas for the coefficients a and az in terms of x and
20
y.)
(c) Describe span {V1, V2} within R2 using words and pictures.
(d) Are the vectors (V1, V2} linearly independent? Justify your answer.
(e) Is the matrix V1 V2 invertible? If so, find its inverse. How is this connected to your work above?
Vi
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