Let a : V → W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and W₁, W2, W3 a basis of W. Suppose that the corresponding matrix with respect to02 -1 00 -1 01-1 0 3 3What are a (v₁) for i = 1, 2, 3, 4 as elements of W?these bases is A =Select one:a(v₁) = W₂ w3, α(v₂) = 2w₁, a(v3) = −W₁ - W₂ +3w3, a(v₁) = 3w3ONone of the others applyThis is not possible as the matrix A is 3 x 4 so only three of the a(v₂) can be defined by ita(v₁) = W₂ - w3, α(v₂) = W₁ — W3, a(v3) = −w₁ + 3w3, a(v₁) = 3w3Oa(v₁) = W₁ w3, α(v₂) = w₁ +3w₂ +3w3, a(v3) = 2w₂, α(v₁) = w₁ +2w3

Let be a linear map for vector spaces V, W over , a basis of V and a basis of W.Suppose that the…

Let a : V→ W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and w₁, W2, W3 a basis of W. Suppose that the corresponding matrix with respect to 0 2 -1 0 1 0 -1 0 -1 0 3 3 What are a (v;) for i = 1, 2, 3, 4 as elements of W? these bases is A = Select one: O a(v₁) = W₂w3, a(v₂) = 2w₁, a(v3) = −W₁ - W₂ + 3w3, a(v₁) = 3w3 None of the others apply This is not possible as the matrix A is 3 x 4 so only three of the a(vi) can be defined by it O a(v₁) = W₂ - w3, α(v₂) = W₁ — W3, α(v3) = −w₁ +3w3, α(v₁) = 3w3 Ⓒa(v₁) = 2₁ w3, a(v₂) = w₁ +3w₂ +3w3, a(v3) = 2w2, a(v₁) = W₁ + 2w3

Let a : V→ W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and w₁, W2, W3 a basis of W. Suppose that the corresponding matrix with respect to 0 2 -1 0 1 0 -1 0 -1 0 3 3 What are a (v;) for i = 1, 2, 3, 4 as elements of W? these bases is A = Select one: O a(v₁) = W₂w3, a(v₂) = 2w₁, a(v3) = −W₁ - W₂ + 3w3, a(v₁) = 3w3 None of the others apply This is not possible as the matrix A is 3 x 4 so only three of the a(vi) can be defined by it O a(v₁) = W₂ - w3, α(v₂) = W₁ — W3, α(v3) = −w₁ +3w3, α(v₁) = 3w3 Ⓒa(v₁) = 2₁ w3, a(v₂) = w₁ +3w₂ +3w3, a(v3) = 2w2, a(v₁) = W₁ + 2w3

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 24EQ

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