Answered: Let "orthogonal" be defined with… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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Question:
Let "orthogonal" be defined with respect to
the L² inner product on domain [0,1].
(a) Show that po=1 and p₁-1/2-x are
orthogonal.
(b) Find a quadratic polynomial p₂(x) that is
orthogonal to po(x) and p₁(x).
(Therefore, {po,P₁, P2} is a basis for the space
of quadratic polynomials on domain [0,1], and
it is an orthogonal basis with respect to the
chosen inner product).
(c) Suppose a polynomial P(x) is to be written
in the pi basis as P=C₁p₁+C₂P2+C3P3. Give a
formula for each coefficient ci in terms of the
inner product (...)L².

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