8. Let A = {a₁, A₂, A3} and B = {b₁,b₂, b3} be bases for a vector space V, and suppose α₁ = 4b₁ b₂, A₂ = −b₁ + b₂ + b3, and a3 = b₂ − 2b3. Find the change-of-coordinates matrix from A to B. Use the matrix to find [x] given x = 3a₁ + 4a₂ + a3.
8. Let A = {a₁, A₂, A3} and B = {b₁,b₂, b3} be bases for a vector space V, and suppose α₁ = 4b₁ b₂, A₂ = −b₁ + b₂ + b3, and a3 = b₂ − 2b3. Find the change-of-coordinates matrix from A to B. Use the matrix to find [x] given x = 3a₁ + 4a₂ + a3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the change-of-coordinates matrix from A to B, and use the matrix to find [x]B given x = 3a1 + 4a2 = a3. Any help would be appreciated, and thanks in advance.
![8. Let A = {a₁, A2, A3} and B = {b₁,b2, b3} be bases for a vector space V, and suppose
a₁ = 4b₁ — b₂, A₂ = −b₁ + b₂ + b3, and a3 = b₂ − 2b3. Find the change-of-coordinates
matrix from A to B. Use the matrix to find [x] given x = 3a₁ + 4a₂ + a3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05ceb8e8-ee3e-4aa1-a75b-b48c59facb6f%2Fbb762583-74db-4c88-bbfd-555cd1c98206%2Fpa7l2t9_processed.png&w=3840&q=75)
Transcribed Image Text:8. Let A = {a₁, A2, A3} and B = {b₁,b2, b3} be bases for a vector space V, and suppose
a₁ = 4b₁ — b₂, A₂ = −b₁ + b₂ + b3, and a3 = b₂ − 2b3. Find the change-of-coordinates
matrix from A to B. Use the matrix to find [x] given x = 3a₁ + 4a₂ + a3.
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