Example 1.8. Fix a domain D, and let V be the set of all functions f(t)...

Example 1.8. Fix a domain D, and let V be the set of all functions f(t) defined
on D. Define addition and scalar multiples as with polynomials for all t ∈ D:

(f + g)(t) = f(t) + g(t)
(cf)(t) = cf(t)

Then V is a vector space as well, the axioms are verified similarly to those for Pn.

Verify that V in the previous example satisfies the axioms for a vector space.

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Expert Solution

Colby Messinger answered 11 months ago

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