Consider the set S = {2x² + 1, 2x -4, -2x² + x}. The set S spans P₂. If t(x) = 4x² - 2x + 12 € P2, then t can be written as a linear combination of elements of S. That is, t(x) = a · (2x² + 1) + b. (2x-4)+c. (−2x² + x). Determine a, b, and c a b= C

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
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ChapterP: Prerequisites
SectionP.3: Polynomials And Special Products
Problem 8ECP: Find the product of x2+3y and x23y.
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Consider the set S = {2x² + 1, 2x -4, -2x² + x}. The set S spans P₂.
If t(x) = 4x² - 2x + 12 € P2,
then t can be written as a
linear combination of elements of S.
That is,
t(x) = a · (2x² + 1) + b. (2x-4)+c. (−2x² + x).
Determine a, b, and c
a
b=
C
Transcribed Image Text:Consider the set S = {2x² + 1, 2x -4, -2x² + x}. The set S spans P₂. If t(x) = 4x² - 2x + 12 € P2, then t can be written as a linear combination of elements of S. That is, t(x) = a · (2x² + 1) + b. (2x-4)+c. (−2x² + x). Determine a, b, and c a b= C
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