If q(x) is an arbitrary polynomial in Pn it follows that q(x) = c0p0(x) + ... + cnpn(x) (1) for some scalars c0, ... , cn (a) Show that ci = q ( ai) for i = 0, ... , n, and deduce that q(x) = q (a0)p0(x) + · · · + q( an)pn(x) is the unique representation of q(x) with respect to the basis ẞ
If q(x) is an arbitrary polynomial in Pn it follows that q(x) = c0p0(x) + ... + cnpn(x) (1) for some scalars c0, ... , cn (a) Show that ci = q ( ai) for i = 0, ... , n, and deduce that q(x) = q (a0)p0(x) + · · · + q( an)pn(x) is the unique representation of q(x) with respect to the basis ẞ
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 58RE
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If q(x) is an arbitrary polynomial in Pn it follows that q(x) = c0p0(x) + ... + cnpn(x) (1) for some scalars c0, ... , cn (a) Show that ci = q ( ai) for i = 0, ... , n, and deduce that q(x) = q (a0)p0(x) + · · · + q( an)pn(x) is the unique representation of q(x) with respect to the basis ẞ
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