2)Let V₁, V2, W be vector spaces over F. Show that the set Bil(V₁ x V₂, W) ofbilinear maps is a vector space under point-wise addition/scalar multiplication (ie: given f,g bilinear define f + g to be (f+g)(v₁, 2) = f(v₁, v₂) + g(v₁, v₂) and similarly for scalarmultiplication)Solution:

Please check step 2 and 3 for solution.! We will verify axioms of vector space.

Answered: 2) Let V₁, V2, W be vector spaces over…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2) Let V₁, V2, W be vector spaces over F. Show that the set Bil(V₁ x 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, 2) = f(v₁, ₂) + 9(v₁, v2) and similarly for scalar multiplication)