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Problem 1 Let (e1,e2, e3} be a basis for a three-dimensional vector space V. Let A be a linear transformation on V such that A(e₁) e₁, A(e₂) = ₁ + e₂, A(es) = ₁ + ₂ + ez. Show that A is an automorphism and find its inverse.

Problem 1 Let (e1,e2, e3} be a basis for a three-dimensional vector space V. Let A be a linear transformation on V such that A(e₁) e₁, A(e₂) = ₁ + e₂, A(es) = ₁ + ₂ + ez. Show that A is an automorphism and find its inverse.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 16CM
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Problem 1 Let {e₁,e2, e3} be a basis for a three-dimensional vector space V. Let A be a linear transformation on V such that A(e₁) e₁, A(e₂) = ₁ + e2, A(e3) = ₁ + ₂ + €3. Show that A is an automorphism and find its inverse.
Transcribed Image Text:Problem 1 Let {e₁,e2, e3} be a basis for a three-dimensional vector space V. Let A be a linear transformation on V such that A(e₁) e₁, A(e₂) = ₁ + e2, A(e3) = ₁ + ₂ + €3. Show that A is an automorphism and find its inverse.
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