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?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.3: Change Of Basis

Problem 22EQ

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