Let D = {d₁.d₂.d3} and F = {f₁.f2.f3} be bases for a vector space V, and suppose f₁ = 5d₁-d₂ +6d3. f₂ = 4d₂ +d3. f3 = -4d₁ +2d3- a. Find the change-of-coordinates matrix from F to D. b. Find [x]D for x=f₁-5f₂ +5f3.
Let D = {d₁.d₂.d3} and F = {f₁.f2.f3} be bases for a vector space V, and suppose f₁ = 5d₁-d₂ +6d3. f₂ = 4d₂ +d3. f3 = -4d₁ +2d3- a. Find the change-of-coordinates matrix from F to D. b. Find [x]D for x=f₁-5f₂ +5f3.
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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![Let D = {d₁.d₂.d3} and F = {f₁.f2.f3} be bases for a vector space V, and suppose f₁ = 5d₁-d₂ +6d3,
f₂ = 4d₂ +d3, f3 = -4d₁ +2d3.
a. Find the change-of-coordinates matrix from F to D.
b. Find [x]D for x=f₁-5f₂ +5f3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F235c04dd-9366-4463-b266-6e90e6c61d4b%2F234ad526-ee41-425a-89a0-e7a4392fc47f%2F5zy3bnb_processed.png&w=3840&q=75)
Transcribed Image Text:Let D = {d₁.d₂.d3} and F = {f₁.f2.f3} be bases for a vector space V, and suppose f₁ = 5d₁-d₂ +6d3,
f₂ = 4d₂ +d3, f3 = -4d₁ +2d3.
a. Find the change-of-coordinates matrix from F to D.
b. Find [x]D for x=f₁-5f₂ +5f3.
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