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Consider the polynomials p₁ (t) = 2 + 5t, p₂ (t) = 2 − 5t, and p3 (t) = 4 (for all t). By inspection, write a linear dependence relation among P₁, P2, and p3. Then find a basis for Span {P₁, P2, P3}.

Consider the polynomials p₁ (t) = 2 + 5t, p₂ (t) = 2 − 5t, and p3 (t) = 4 (for all t). By inspection, write a linear dependence relation among P₁, P2, and p3. Then find a basis for Span {P₁, P2, P3}.

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 polynomials \( p_1(t) = 2 + 5t \), \( p_2(t) = 2 - 5t \), and \( p_3(t) = 4 \) (for all \( t \)). By inspection, write a linear dependence relation among \( \mathbf{p_1} \), \( \mathbf{p_2} \), and \( \mathbf{p_3} \). Then find a basis for Span \(\{\mathbf{p_1}, \mathbf{p_2}, \mathbf{p_3}\}\).
Transcribed Image Text:Consider the polynomials \( p_1(t) = 2 + 5t \), \( p_2(t) = 2 - 5t \), and \( p_3(t) = 4 \) (for all \( t \)). By inspection, write a linear dependence relation among \( \mathbf{p_1} \), \( \mathbf{p_2} \), and \( \mathbf{p_3} \). Then find a basis for Span \(\{\mathbf{p_1}, \mathbf{p_2}, \mathbf{p_3}\}\).
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