Question: The polynomials p(x) = x(x − 1) and q(x) = ½ (x − 1)(x − 2) are orthogonal when the inner product is defined by (p(x), q(x)) = p(0)q(0) + p(1)q(1) +p(2)q(2). What is the distance between these vectors using the norm determined by the same inner product?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Question:** The polynomials \( p(x) = \frac{1}{2} x (x - 1) \) and \( q(x) = \frac{1}{2} (x - 1)(x - 2) \) are orthogonal when the inner product is defined by 

\[
\langle p(x), q(x) \rangle = p(0)q(0) + p(1)q(1) + p(2)q(2).
\]

What is the distance between these vectors using the norm determined by the same inner product?
Transcribed Image Text:**Question:** The polynomials \( p(x) = \frac{1}{2} x (x - 1) \) and \( q(x) = \frac{1}{2} (x - 1)(x - 2) \) are orthogonal when the inner product is defined by \[ \langle p(x), q(x) \rangle = p(0)q(0) + p(1)q(1) + p(2)q(2). \] What is the distance between these vectors using the norm determined by the same inner product?
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