2.Let P3(IR) be the vector space of all polynomials of degree 3 or less (and the zeropolynomial). Determine whether p(x) = x³ – 5 + 8 is in the subspace (S), whereS = {67x* + x² + 9x + 4, 10x³ – 50x² + x + 6, 7x³ + 23x² – x + 17}.

Answered: Image /qna-images/answer/4322b9e2-f317-4d39-bc28-b7ea4380770c.jpg

Answered: 2. Let P3(R) be the vector space of all…

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 P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by −(4x2+5x+4), 1−(6x2+17x) and −(x2+2). The dimension of the subspace H is . Is {−(4x2+5x+4),1−(6x2+17x),−(x2+2)} a basis for P2? choose Be sure you can explain and justify your answer. A basis for the subspace H is { }. Enter a polynomial or a comma separated list of polynomials
O -2x (3) A. 7x XER 5x -{]-*-*-*-²} B. y - 7x - 5y - 4z Which of the following sets are subspaces of R³ ? C. ● Z F. X x + 3 x - 8 ● X •{:) -->0} D. y Z | XER} X = { ;] x + y + ² = 0 } E. X Z X {] Z - 3x + 8y = 0 & 6x2z =
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2. Let P3(R) be the vector space of all polynomials of degree 3 or less (and the zero polynomial). Determine whether p(x) = x³ – 5x + 8 is in the subspace (S), where S = {67x* + x² + 9x + 4, 10x³ – 50x² + x + 6, 7x* + 23x² – x + 17}.