Consider the set S = {1+3x+x²,-1+x+2x²,4x} a) S is a basis for P2. b) S is not a basis for P₂ since it is not linearly independent. c) S is not a basis for P2 since it is not a spanning set.
Consider the set S = {1+3x+x²,-1+x+2x²,4x} a) S is a basis for P2. b) S is not a basis for P₂ since it is not linearly independent. c) S is not a basis for P2 since it is not a spanning set.
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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Transcribed Image Text:Consider the set S = {1+3x+x²,-1+x+2x²,4x}
a) S is a basis for P₂.
b) S is not a basis for P₂ since it is not linearly independent.
c) S is not a basis for P2 since it is not a spanning set.
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