a) Let P: the vector space of all polynomials of degree 2. Prove that W= (p = Pz: p(1) = 2 p(0)) is a subspace of P:. b) Let G=Span{(1, 1, 0), (1, 0, 1)). If the vector v = (m. - (1+m), -m) belongs to G. Find the value of m.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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a) Let P: the vector space of all polynomials of degree ≤ 2.
Prove that W= (p = P₂: p(1) = 2 p(0)) is a subspace of P:.
b) Let G=Span{(1, 1, 0), (1, 0, 1)). If the vector v = (m. - (1+m), -m) belongs to G. Find the value of m.
Transcribed Image Text:a) Let P: the vector space of all polynomials of degree ≤ 2. Prove that W= (p = P₂: p(1) = 2 p(0)) is a subspace of P:. b) Let G=Span{(1, 1, 0), (1, 0, 1)). If the vector v = (m. - (1+m), -m) belongs to G. Find the value of m.
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