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Let H be the subspace of P2 spanned by x2 – 3, – 1 and x² + 1.

Let H be the subspace of P2 spanned by x2 – 3, – 1 and x² + 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let H be the subspace of P2P2 spanned by ?2−3, −1x2−3, −1 and ?2+1x2+1.

(a) A basis for H is {{  }}.
Enter a polynomial or a list of polynomials separated by commas, in terms of lower-case x . For example x+1,x-2

(b) The dimension of H is  .

(c) Is {?2−3,−1,?2+1}{x2−3,−1,x2+1} a basis for P2P2?

(2 points) Let H be the subspace of P2 spanned by x2 – 3, - 1 and x? + 1. (a) A basis for H is { }. Enter a polynomial or a list of polynomials separated by commas, in terms of lower-case x . For example x+1,x-2 (b) The dimension of H is (c) Is {x² – 3, –1, x² + 1} a basis for P2?
Transcribed Image Text:(2 points) Let H be the subspace of P2 spanned by x2 – 3, - 1 and x? + 1. (a) A basis for H is { }. Enter a polynomial or a list of polynomials separated by commas, in terms of lower-case x . For example x+1,x-2 (b) The dimension of H is (c) Is {x² – 3, –1, x² + 1} a basis for P2?
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