Let V₁, V2, and V3 be vector spaces and T₁ : V₁ → V₂ and T2 : V2 → V3 be linear transforma- tions. Show that T₂ 0 T₁ : V₁ → V3 is a linear transformation by verifying: O (a) If v, w € V₁ are vectors then T₂ 0 T₁(v + w) = T₂ 0 T₁(v) + T₂ ° T₁(w) O O O (b) If v € V₁ is a vector and c E R is a scalar then T₂ 0 T₁(cv) = c(T₂ 0 T₁ (v)).

Let V₁, V2, and V3 be vector spaces and T₁ : V₁ → V₂ and T2 : V2 → V3 be linear transforma- tions. Show that T₂ 0 T₁ : V₁ → V3 is a linear transformation by verifying: O (a) If v, w € V₁ are vectors then T₂ 0 T₁(v + w) = T₂ 0 T₁(v) + T₂ ° T₁(w) O O O (b) If v € V₁ is a vector and c E R is a scalar then T₂ 0 T₁(cv) = c(T₂ 0 T₁ (v)).

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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