Let H be the set of polynomials (a) Give two different examples of polynomials in H. example 1: p(x) = example 2: q(x) = (b) Give two different examples of polynomials from P3 which are not in H. example 1: p(x) = example 2: q(x) = (c) Complete the following statements to determine if H is a subspace of P3. in H. 0 ? H is ? ◆ under vector addition. If it is not closed, enter two polynomials p, q E H below, whose sum is not in Ħ. If it is closed, then leave the following spaces blank. p(x) = q(x) = H = {p = P3 | P(2) = 0}. His ? under scalar multiplication. If it is not closed, enter a scalar k and polynomial r E H below, whose product is not in H. If it is closed, then leave the following spaces blank. and r(x) = k = H ? ◆ of P3.

Let H be the set of polynomials (a) Give two different examples of polynomials in H. example 1: p(x) = example 2: q(x) = (b) Give two different examples of polynomials from P3 which are not in H. example 1: p(x) = example 2: q(x) = (c) Complete the following statements to determine if H is a subspace of P3. in H. 0 ? H is ? ◆ under vector addition. If it is not closed, enter two polynomials p, q E H below, whose sum is not in Ħ. If it is closed, then leave the following spaces blank. p(x) = q(x) = H = {p = P3 | P(2) = 0}. His ? under scalar multiplication. If it is not closed, enter a scalar k and polynomial r E H below, whose product is not in H. If it is closed, then leave the following spaces blank. and r(x) = k = H ? ◆ of P3.

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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