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4. The set {1, x" | n E N} is a basis for R[æ] as a vector space over R. R[r] = {ao + a1x + a2x2 + ...+ a,x" | n e Z® and a; eR for all i = 0, 1, 2, - .. , n}

4. The set {1, x" | n E N} is a basis for R[æ] as a vector space over R. R[r] = {ao + a1x + a2x2 + ...+ a,x" | n e Z® and a; eR for all i = 0, 1, 2, - .. , n}

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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4. The set {1, r" | n E N} is a basis for R[r] as a vector space over R. R[r] = {ao + a1r + azx? + ...+ a,r" | n E Z® and a; ER for all i = 0, 1, 2, -.. ,n}
Transcribed Image Text:4. The set {1, r" | n E N} is a basis for R[r] as a vector space over R. R[r] = {ao + a1r + azx? + ...+ a,r" | n E Z® and a; ER for all i = 0, 1, 2, -.. ,n}
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