Using only the definition of a linear map (Definition 3.2 in the textbook) and the properties of vector spaces. Let VV and WW be vector spaces over FF. Prove that a function T:V→WT:V→W is a linear map if and only if T(λu+αv)=λT(u)+αT(v)T(λu+αv)=λT(u)+αT(v) for every λ,α∈Fλ,α∈F and u,v∈Vu,v∈V.

Using only the definition of a linear map (Definition 3.2 in the textbook) and the properties of vector spaces. Let VV and WW be vector spaces over FF. Prove that a function T:V→WT:V→W is a linear map if and only if T(λu+αv)=λT(u)+αT(v)T(λu+αv)=λT(u)+αT(v) for every λ,α∈Fλ,α∈F and u,v∈Vu,v∈V.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

See similar textbooks