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Consider the set S = {x² + 1, 2x − 2, − x² + x}. The set S spans P2. If t(x) = = 2x² 16x + 10 € P₂, then t can be written as a linear combination of elements of S. That is, t(x) = a. Determine a, b, and c a = — (x² +1) + b ⋅ (2x − 2) + c · (–x² + x). b - C =

Consider the set S = {x² + 1, 2x − 2, − x² + x}. The set S spans P2. If t(x) = = 2x² 16x + 10 € P₂, then t can be written as a linear combination of elements of S. That is, t(x) = a. Determine a, b, and c a = — (x² +1) + b ⋅ (2x − 2) + c · (–x² + x). b - C =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2. If t(x) = = 2x² 16x + 10 € P₂, — then t can be written as a linear combination of elements of S. That is, t(x) = a. Determine a, b, and c a = (x² + 1) + b · (2x − 2) + c · (−x² + x). b - C =
Transcribed Image Text:Consider the set S = {x² + 1, 2x − 2, −x² + x}. The set S spans P2. If t(x) = = 2x² 16x + 10 € P₂, — then t can be written as a linear combination of elements of S. That is, t(x) = a. Determine a, b, and c a = (x² + 1) + b · (2x − 2) + c · (−x² + x). b - C =
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