Let P, be the vector space of all polynomials of degree < 2. If W is the set of all polynomials of the form a, + a,x + azx² such that a, – a, + az = 0. Determine whether W is a subspace of P2. Hint, W = {(a, + a,x + a,x²)|a, – a, +az = 0}.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 45E: Consider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less...
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Let P, be the vector space of all polynomials of degree < 2. If W is the set of all
polynomials of the form a, + a,x + azx² such that ao – az + az = 0.
Determine whether W is a subspace of P2.
Hint, W = {(a, + a,x + azx²)|a, – az + az = 0}.
Transcribed Image Text:Let P, be the vector space of all polynomials of degree < 2. If W is the set of all polynomials of the form a, + a,x + azx² such that ao – az + az = 0. Determine whether W is a subspace of P2. Hint, W = {(a, + a,x + azx²)|a, – az + az = 0}.
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