(10) Let TV → W be a linear transformation and let B = {a₁, 02,..., an} bea spanning set for V. Prove that the set T(B) = {T(α₁), T(α₂),...,T(an)} spansthe range of T.

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Answered: (10) Let TV → W be a linear…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 19EQ

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(10) Let TV → W be a linear transformation and let B = {a₁, a2,..., an} be a spanning set for V. Prove that the set T(B) = {T(α₁), T(α₂),...,T(an)} spans the range of T.