Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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 \( \mathbb{R} \)).
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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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