Consider the vector space V = {p(x) = ao +ajr+azx² | a¡ € R, deg(p(æ)) < 2} of polynomials of degree less than or equal to 2, with the pointwise addition and scalar multiplication. Show that W = {p(x) € V : p(1) = 0} is a subspace of V.
Consider the vector space V = {p(x) = ao +ajr+azx² | a¡ € R, deg(p(æ)) < 2} of polynomials of degree less than or equal to 2, with the pointwise addition and scalar multiplication. Show that W = {p(x) € V : p(1) = 0} is a subspace of V.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.CR: Review Exercises
Problem 73CR
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Consider the
V = {p(x) = a0 + a1x + a2x2 | ai ∈ R, deg(p(x)) ≤ 2}
of polynomials of degree less than or equal to 2, with
the pointwise addition and scalar multiplication. Show
that W = {p(x) ∈ V : p(1) = 0} is a subspace of V .
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