Consider the set S = {4x + 1, 2x - 8, 4x + a}. The set S spans P2. - If t(x) = 8x-9x +43 e P2, then t can be written as a linear combination of elements of S. That is, t(x) = a· (4a2 + 1) +b (2 - 8) +c (-4x2+ a). Determine a, b, and c a = b =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 15E
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Consider the set S = {4x + 1, 2x 8,
4x + a}. The set S spans P2.
%3D
If t(x) = 8x - 9a +43 e P2,
then t can be written as a
linear combination of elements of S.
That is,
t(x) :
(4a + 1) + b. (2a – 8) + c (-4x2 + a).
= a.
Determine a, b, and c
a =
b.
C =
%3D
Transcribed Image Text:Consider the set S = {4x + 1, 2x 8, 4x + a}. The set S spans P2. %3D If t(x) = 8x - 9a +43 e P2, then t can be written as a linear combination of elements of S. That is, t(x) : (4a + 1) + b. (2a – 8) + c (-4x2 + a). = a. Determine a, b, and c a = b. C = %3D
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