Let D = (d₁.d₂.d3) and F= {f₁.f2.13) be bases for a vector space V, and suppose f₁ = 6d, -d₂ +4d3, f₂=d₂ +d3, f3 3d, +4d3. a. Find the change-of-coordinates matrix from F to D. b. Find [x]p for x = 1₁-3f₂ +3f3. a. P = D+F

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...
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Let D = (d₁.d₂.d3) and F= {f₁.f2.13) be bases for a vector space V, and suppose f₁ = 6d, -d₂ +4d3, f₂=d₂ +d3,
f3= -3d₁ +4d3.
a. Find the change-of-coordinates matrix from F to D.
b. Find [x]p for x=1₁-3f₂ +3f3.
a. P =
D+F
Transcribed Image Text:Let D = (d₁.d₂.d3) and F= {f₁.f2.13) be bases for a vector space V, and suppose f₁ = 6d, -d₂ +4d3, f₂=d₂ +d3, f3= -3d₁ +4d3. a. Find the change-of-coordinates matrix from F to D. b. Find [x]p for x=1₁-3f₂ +3f3. a. P = D+F
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