5. Consider the vector space P2(R), the set of all polynomial func- tions of degree less than or equal to 2 with real coefficients. Show that the set S = {a.u² + bx + c€ P2(R) | a+b = c} is a subspace of P(R). %3D

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5. Consider the vector space P2(R), the set of all polynomial func-
tions of degree less than or equal to 2 with real coefficients.
Show that the set S = {a.x2 + bx +c E P2(R) | a+b c} is
a subspace of P2(R).
Transcribed Image Text:5. Consider the vector space P2(R), the set of all polynomial func- tions of degree less than or equal to 2 with real coefficients. Show that the set S = {a.x2 + bx +c E P2(R) | a+b c} is a subspace of P2(R).
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