Let V be a vector space over F and assume that the maps f : V → F and f2 : V → F be lincar transformations (Note that any ficld F can be considered a vector space over itsclf). Define T : V –→ F² by T(v) = (fi(v), f2(v)). Prove that T is a linear transformation.
Let V be a vector space over F and assume that the maps f : V → F and f2 : V → F be lincar transformations (Note that any ficld F can be considered a vector space over itsclf). Define T : V –→ F² by T(v) = (fi(v), f2(v)). Prove that T is a linear transformation.
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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![Let V be a vector space over F and assume that the maps fi : V → F and f2 : V → F
be linear transformations (Note that any field F can be considered a vector space over itself).
Define T : V –→ F² by T(v) = (fi(v), f2(v)). Prove that T is a linear transformation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bdb540a-50ee-4458-a770-17b9fda54b9c%2Fd6b9ae18-fb93-4db0-b263-0d0be9e39f14%2F6q7jqf_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be a vector space over F and assume that the maps fi : V → F and f2 : V → F
be linear transformations (Note that any field F can be considered a vector space over itself).
Define T : V –→ F² by T(v) = (fi(v), f2(v)). Prove that T is a linear transformation.
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