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(a) U={p (b) U={p (c) U = {p R2[x] | p(1) = p(−1) = 0}, N = {x²-1}. R2[x] | p(1) = p'(0)}, = {1-x2, x}. R2[x] | p(1) = p(2) = p(3)}, N = {2}. (d) U = {p (e) U={p R2[x] | p'(1) = p"(1)}, N = {1, 2}. R2[x] | p(1) = p(-1)}, N = {1+x2}.

(a) U={p (b) U={p (c) U = {p R2[x] | p(1) = p(−1) = 0}, N = {x²-1}. R2[x] | p(1) = p'(0)}, = {1-x2, x}. R2[x] | p(1) = p(2) = p(3)}, N = {2}. (d) U = {p (e) U={p R2[x] | p'(1) = p"(1)}, N = {1, 2}. R2[x] | p(1) = p(-1)}, N = {1+x2}.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1YT
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For which of the following pairs is the set Ω not a basis for the vector subspace U ≤ R2[x]?

 

(a) U={p (b) U={p (c) U = {p R2[x] | p(1) = p(−1) = 0}, N = {x²-1}. R2[x] | p(1) = p'(0)}, = {1-x2, x}. R2[x] | p(1) = p(2) = p(3)}, N = {2}. (d) U = {p (e) U={p R2[x] | p'(1) = p"(1)}, N = {1, 2}. R2[x] | p(1) = p(-1)}, N = {1+x2}.
Transcribed Image Text:(a) U={p (b) U={p (c) U = {p R2[x] | p(1) = p(−1) = 0}, N = {x²-1}. R2[x] | p(1) = p'(0)}, = {1-x2, x}. R2[x] | p(1) = p(2) = p(3)}, N = {2}. (d) U = {p (e) U={p R2[x] | p'(1) = p"(1)}, N = {1, 2}. R2[x] | p(1) = p(-1)}, N = {1+x2}.
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