1. Decide if p lies in the span of {v1, v2, v3}. If it does, find a linear combination that makes the vector. If it does not, show that no linear combination exists. p(x) = x − x³, v₁(x) = x², v2(x) = 2x + x², v3(x) = x+x³.
1. Decide if p lies in the span of {v1, v2, v3}. If it does, find a linear combination that makes the vector. If it does not, show that no linear combination exists. p(x) = x − x³, v₁(x) = x², v2(x) = 2x + x², v3(x) = x+x³.
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:1. Decide if p lies in the span of {v1, v2, v3}. If it does, find a linear combination that makes the vector.
If it does not, show that no linear combination exists.
p(x) = x − x³, v₁(x) = x², v2(x) = 2x + x², v3(x) = x+x³.
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