Consider the set S = {2x² + 1, 2x – 4, 2x + x}. The set S spans P2. If t(a) — 6а? + 6х — 15 € Ра, 6x? + 6x – 15 e P2 , then t can be written as a linear combination of elements of S. That is, t(x) = — а - (2л + 1) +b . (2ӕ — 4) + с : (- 2»? + а). Determine a, b, and c a = 6 = C =
Consider the set S = {2x² + 1, 2x – 4, 2x + x}. The set S spans P2. If t(a) — 6а? + 6х — 15 € Ра, 6x? + 6x – 15 e P2 , then t can be written as a linear combination of elements of S. That is, t(x) = — а - (2л + 1) +b . (2ӕ — 4) + с : (- 2»? + а). Determine a, b, and c a = 6 = C =
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 \( S = \{2x^2 + 1, 2x - 4, -2x^2 + x\} \). The set \( S \) spans \( P_2 \).
If \( t(x) = 6x^2 + 6x - 15 \in P_2 \),
then \( t \) can be written as a linear combination of elements of \( S \).
That is,
\[ t(x) = a \cdot (2x^2 + 1) + b \cdot (2x - 4) + c \cdot (-2x^2 + x). \]
Determine \( a, b, \) and \( c \).
\[ a = \underline{\phantom{0}} \quad b = \underline{\phantom{0}} \quad c = \underline{\phantom{0}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5025798a-663c-4f82-a82a-d0677c58328a%2F45c1cb47-a18e-4fa1-9d03-12a700719d9a%2Fl0nhiib_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the set \( S = \{2x^2 + 1, 2x - 4, -2x^2 + x\} \). The set \( S \) spans \( P_2 \).
If \( t(x) = 6x^2 + 6x - 15 \in P_2 \),
then \( t \) can be written as a linear combination of elements of \( S \).
That is,
\[ t(x) = a \cdot (2x^2 + 1) + b \cdot (2x - 4) + c \cdot (-2x^2 + x). \]
Determine \( a, b, \) and \( c \).
\[ a = \underline{\phantom{0}} \quad b = \underline{\phantom{0}} \quad c = \underline{\phantom{0}} \]
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