V is a 3-dimensional vector space with basis By (V1, V2, V3) and W is a 3-dimensional vector space with basis Bw (w₁, W2, w3). Let x₁ = w₁ +2w2 +3w3, x2 = w₁ +4w₂ +7w3, 23 = = 3w₁ +2w₂+w3, x3 =W₁-2w2 - 5w3, x3 = w₁+w₂+W3. T, T, T* are three linear transformations from V to W and satisfy; T(v₁)= T'(v₁) T* (v₁) = x₁ T(v₂)=T'(v₂) = T* (v₂) = x₂ T(v3) = x3, T'(v3) = x3, T* (v3) = x3. Determine which of these transformations is an isomorphism?
V is a 3-dimensional vector space with basis By (V1, V2, V3) and W is a 3-dimensional vector space with basis Bw (w₁, W2, w3). Let x₁ = w₁ +2w2 +3w3, x2 = w₁ +4w₂ +7w3, 23 = = 3w₁ +2w₂+w3, x3 =W₁-2w2 - 5w3, x3 = w₁+w₂+W3. T, T, T* are three linear transformations from V to W and satisfy; T(v₁)= T'(v₁) T* (v₁) = x₁ T(v₂)=T'(v₂) = T* (v₂) = x₂ T(v3) = x3, T'(v3) = x3, T* (v3) = x3. Determine which of these transformations is an isomorphism?
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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Transcribed Image Text:V is a 3-dimensional vector space with basis By (V1, V2, V3) and W is a
3-dimensional vector space with basis Bw (w₁, W2, w3). Let
x₁ = w₁ +2w2 +3w3, x2 = w₁ +4w₂+7w3,
23 = = 3w₁ +2w₂+w3, x3 =W₁ - 2w2 - 5w3, x3 =w₁+w₂w3.
T, T', T* are three linear transformations from V to W and satisfy;
T(v₁) T'(v₁) T* (v₁) = x₁
=
T(v₂)= T'(v₂) = 7* (v₂) = x₂
T(v3) = x3, T' (v3) = x3, T* (v3) = x3.
Determine which of these transformations is an isomorphism?
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