Let M be the set of all vectors (or polynomials) x in p (over R) for which x(t)=x(-t) - even polynomial functions – holds identically in t. Show that M is a subspace of p (over R)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let \( M \) be the set of all vectors (or polynomials) \( x \) in \( \mathscr{P} \) (over \( \mathbb{R} \)) for which \( x(t) = x(-t) \)—even polynomial functions—holds identically in \( t \). Show that \( M \) is a subspace of \( \mathscr{P} \) (over \( \mathbb{R} \)).
Transcribed Image Text:Let \( M \) be the set of all vectors (or polynomials) \( x \) in \( \mathscr{P} \) (over \( \mathbb{R} \)) for which \( x(t) = x(-t) \)—even polynomial functions—holds identically in \( t \). Show that \( M \) is a subspace of \( \mathscr{P} \) (over \( \mathbb{R} \)).
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Subspace test:

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