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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 19E
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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