1 Let P = -3 -5 4 3 -1 0 5 1 U₁² = V1 ₁4₂ = ₁ 43 = - 3 2 V₂ -7 4, and V3 = 3 a. Find a basis {U₁, U₂, U3} for R³ such that P is the change-of-coordinates matrix from {u₁, U₂, U3} to the basis {V₁, V2, V3}. [Hint: What do the columns of P_ represent?] C+B -9 4. Complete parts (a) and (b). 7
1 Let P = -3 -5 4 3 -1 0 5 1 U₁² = V1 ₁4₂ = ₁ 43 = - 3 2 V₂ -7 4, and V3 = 3 a. Find a basis {U₁, U₂, U3} for R³ such that P is the change-of-coordinates matrix from {u₁, U₂, U3} to the basis {V₁, V2, V3}. [Hint: What do the columns of P_ represent?] C+B -9 4. Complete parts (a) and (b). 7
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 69E: Find a basis for R2 that includes the vector (2,2).
Related questions
Question
![Let P =
1
-3 -5
4
5
3 -1
0
1
=
V1
· 4₂ = ₁ 43 =
- 3
2
V2
-7
4, and V3 =
3
...
a. Find a basis {U₁, U₂, U3} for R³ such that P is the change-of-coordinates matrix from {u₁, U₂, U3} to the basis
{V1 V2 V3} [Hint: What do the columns of P represent?]
C + B
-9
4. Complete parts (a) and (b).
7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4f55b02-9097-453c-bad2-7370fd6ef71f%2F7071d15e-8c80-4cd0-9dce-5214daf237ce%2Ffyr30me_processed.png&w=3840&q=75)
Transcribed Image Text:Let P =
1
-3 -5
4
5
3 -1
0
1
=
V1
· 4₂ = ₁ 43 =
- 3
2
V2
-7
4, and V3 =
3
...
a. Find a basis {U₁, U₂, U3} for R³ such that P is the change-of-coordinates matrix from {u₁, U₂, U3} to the basis
{V1 V2 V3} [Hint: What do the columns of P represent?]
C + B
-9
4. Complete parts (a) and (b).
7

Transcribed Image Text:b. Find a basis {W₁, W₂, W3} for R³ such that P is the change-of-coordinates matrix from {V₁ V₂ V3} to (W₁, W₂, W3}
W₁ = ₁ W₂ = ₁ W₁ = [
□
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