7) Let V and W be vector spaces over a field F. Recall L(V,W) denotes the set of all linear transformations from V into W. Describe how we define the operations of vector addition and scalar multiplication so that L(V, W) becomes a vector space over F. You need not prove that L(V,W) is a vector space, only write a clear and complete definition of how to add two vectors of L(V, W), and how to multiply a vector by a scalar element of F. b. Describe how the zero vector in L(V,W) is defined. a.

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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7) Let V and W be vector spaces over a field F. Recall L(V,W) denotes the set of all linear
transformations from V into W.
a. Describe how we define the operations of vector addition and scalar multiplication so
that L(V, W) becomes a vector space over F. You need not prove that L(V,W) is a
vector space, only write a clear and complete definition of how to add two vectors of
L(V, W), and how to multiply a vector by a scalar element of F.
b. Describe how the zero vector in L(V, W) is defined.
Transcribed Image Text:7) Let V and W be vector spaces over a field F. Recall L(V,W) denotes the set of all linear transformations from V into W. a. Describe how we define the operations of vector addition and scalar multiplication so that L(V, W) becomes a vector space over F. You need not prove that L(V,W) is a vector space, only write a clear and complete definition of how to add two vectors of L(V, W), and how to multiply a vector by a scalar element of F. b. Describe how the zero vector in L(V, W) is defined.
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