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1) Let V, W be finite dimensional vector spaces and let B = {v₁,..., Un} be a basis for V. Let T: VW be a linear map. (a) Show that T is surjective T(B) spans W (b) Conclude that T is an isomorphism ⇒ T(B) is a basis for W

1) Let V, W be finite dimensional vector spaces and let B = {v₁,..., Un} be a basis for V. Let T: VW be a linear map. (a) Show that T is surjective T(B) spans W (b) Conclude that T is an isomorphism ⇒ T(B) is a basis for W

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 43EQ
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1) Let V, W be finite dimensional vector spaces and let B = {v₁,..., Un} be a basis for V. Let T: VW be a linear map. (a) Show that T is surjective T(B) spans W (b) Conclude that T is an isomorphism ⇒ T(B) is a basis for W
Transcribed Image Text:1) Let V, W be finite dimensional vector spaces and let B = {v₁,..., Un} be a basis for V. Let T: VW be a linear map. (a) Show that T is surjective T(B) spans W (b) Conclude that T is an isomorphism ⇒ T(B) is a basis for W
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