Let V = R[x] = {p(x): grad (p(x) ≤ n} the vector space of the set of polynomials of degree less than or equal to: n(n E N) and f: R[x] → Ra function given by: f(ao + a₁x + + anx") = ao ... show that f is a homomorphism (linear transformation). Also calculate its kernel and image.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let V =
R[x] = {p(x): grad (p(x) ≤ n} the vector space
of the set of polynomials of degree less than or equal to:
n(n E N) and f: R[x] → R a function given by:
f(a₁ + a₁x + ... + anx") = ao
show that f is a homomorphism (linear transformation).
Also calculate its kernel and image.
Transcribed Image Text:Let V = R[x] = {p(x): grad (p(x) ≤ n} the vector space of the set of polynomials of degree less than or equal to: n(n E N) and f: R[x] → R a function given by: f(a₁ + a₁x + ... + anx") = ao show that f is a homomorphism (linear transformation). Also calculate its kernel and image.
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