14. Let T: X→ Y be a linear operator and dim X=dim Y=n<∞0.Show that R(T) = Y if and only if T¹ exists.

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Answered: Let T: X→→→→→ Y be a linear operator…

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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Let T: X→→→→→ Y be a linear operator and dim X = dim Y=n<∞. Show that R(T) = Y if and only if T¹ exists.