Consider the inner product on P4, the vector space of polynomials of order up to 4, defined as (p(x), q(x)) = p(ao)q(ao) + · · · + p(a4)q(a4) ... with ao -2, a, = -1, a, = 0, az = 1 and as = 2. Using the polynomials Ili#k (x – a;) Il4k (ak – a;)' - SE(x) = k E {0,..,4}, where IIitk is the product over indices in {i E {0, . p(x) = x4 + x2 +1 in the form .., 4}|i # k}, express p(x) = ao 80(x) +… … +a484(x). ... With a precision of up to 3 decimal places, e.g. "4.598" or "6.667", calculate • the value of ao: • the value of 1: • the value of 2: • the value of az: • the value of a4:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the inner product on P4, the vector space of polynomials of order up to 4,
defined as
(p(x), q(x)) = p(ao)q(ao) + · · · + p(a4)q(a4)
...
with ao
-2, a, = -1, a, = 0, az = 1 and as = 2. Using the polynomials
Ili#k (x – a;)
Il4k (ak – a;)'
-
SE(x) =
k E {0,..,4},
where IIitk is the product over indices in {i E {0, .
p(x) = x4 + x2 +1 in the form
..,4}|i # k}, express
p(x) = ao 80(x) +… … +a484(x).
...
With a precision of up to 3 decimal places, e.g. "4.598" or "6.667", calculate
• the value of ao:
• the value of 1:
• the value of 2:
• the value of az:
• the value of a4:
Transcribed Image Text:Consider the inner product on P4, the vector space of polynomials of order up to 4, defined as (p(x), q(x)) = p(ao)q(ao) + · · · + p(a4)q(a4) ... with ao -2, a, = -1, a, = 0, az = 1 and as = 2. Using the polynomials Ili#k (x – a;) Il4k (ak – a;)' - SE(x) = k E {0,..,4}, where IIitk is the product over indices in {i E {0, . p(x) = x4 + x2 +1 in the form ..,4}|i # k}, express p(x) = ao 80(x) +… … +a484(x). ... With a precision of up to 3 decimal places, e.g. "4.598" or "6.667", calculate • the value of ao: • the value of 1: • the value of 2: • the value of az: • the value of a4:
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