Consider the quadrature rule Q[f; -1, 1] = woƒ(−1) + w₁ f(x₁) + w₂ƒ(1) with weights wo,W₁,W₂ER and nodes x₁=-1, X₁€(-1,1) and x2=1. Is it possible to specify wo, W₁, W₂ and X₁ in such a way that the degree of exactness of Q is m=5? If so, what is the product X₁W₁? O a. X₁W₁=-1 Ob. X₁W₁=0 O c. X₁W₁=1 O d. X₁W₁=√2 O e. X₁W₁=√3 O f. X₁W₁=3√2 Og. X₁W₁=3√3 Oh. X₁W₁=3√5 Oi. X₁W₁=5√3 O j. It is impossible to choose wo, W₁, W₂ and x₁ in such a way that the degree of exactness of Q is m=5.
Consider the quadrature rule Q[f; -1, 1] = woƒ(−1) + w₁ f(x₁) + w₂ƒ(1) with weights wo,W₁,W₂ER and nodes x₁=-1, X₁€(-1,1) and x2=1. Is it possible to specify wo, W₁, W₂ and X₁ in such a way that the degree of exactness of Q is m=5? If so, what is the product X₁W₁? O a. X₁W₁=-1 Ob. X₁W₁=0 O c. X₁W₁=1 O d. X₁W₁=√2 O e. X₁W₁=√3 O f. X₁W₁=3√2 Og. X₁W₁=3√3 Oh. X₁W₁=3√5 Oi. X₁W₁=5√3 O j. It is impossible to choose wo, W₁, W₂ and x₁ in such a way that the degree of exactness of Q is m=5.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 58EQ
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![Consider the quadrature rule
Q[f; -1, 1] = wof(−1) + w₁f(x₁) + w₂f(1)
with weights wo,W₁,W₂ER and nodes x。=-1, x₁€(-1,1) and x2=1. Is it possible to specify w₁, W₁, W₂ and ₁ in such a way that the degree of exactness of Q is m=5?
If so, what is the product X₁W₁?
O a. X1W₁=-1
O b. X₁W₁=0
C. X₁W₁=1
O d. W₁=√2
e. X₁W₁=√3
f. x₁W₁=3√2
g. X₁W₁=3√3
Oh. X₁W₁=3√5
Oi. X₁W₁1=5√3
O j. It is impossible to choose wo, W₁, W₂ and X₁ in such a way that the degree of exactness of Q is m=5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe1fc35-672a-49fd-831b-9642c77888ed%2Fe768f2f7-18c6-4449-92ee-57354e0ac26a%2Fezyp0r_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the quadrature rule
Q[f; -1, 1] = wof(−1) + w₁f(x₁) + w₂f(1)
with weights wo,W₁,W₂ER and nodes x。=-1, x₁€(-1,1) and x2=1. Is it possible to specify w₁, W₁, W₂ and ₁ in such a way that the degree of exactness of Q is m=5?
If so, what is the product X₁W₁?
O a. X1W₁=-1
O b. X₁W₁=0
C. X₁W₁=1
O d. W₁=√2
e. X₁W₁=√3
f. x₁W₁=3√2
g. X₁W₁=3√3
Oh. X₁W₁=3√5
Oi. X₁W₁1=5√3
O j. It is impossible to choose wo, W₁, W₂ and X₁ in such a way that the degree of exactness of Q is m=5.
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