2) Let V₁, V2, W be vector spaces over F. Show that the set Bil(V₁ × V₂, W) of bilinear maps is a vector space under point-wise addition/scalar multiplication (ie: given f, g bilinear define f + g to be (f + g) (V₁, V₂) := f(V₁, V2) + g(v₁, v₂) and similarly for scalar multiplication)
2) Let V₁, V2, W be vector spaces over F. Show that the set Bil(V₁ × V₂, W) of bilinear maps is a vector space under point-wise addition/scalar multiplication (ie: given f, g bilinear define f + g to be (f + g) (V₁, V₂) := f(V₁, V2) + g(v₁, v₂) and similarly for scalar multiplication)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...
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