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f₁(x) = x₁ f₂(x) = x², f3(x) = 4x - 2x² g(x) = C₁f₁(x) + C₂f₂(x) + c3f3(x) olve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞o, co). If a nontrivial solution exists, state it. (If only the trivial solution exist =1² C2, C3} = {1,8,8 x } etermine whether f₁, f₂, f3 are linearly independent on the interval (-0, ∞o). Olinearly dependent

f₁(x) = x₁ f₂(x) = x², f3(x) = 4x - 2x² g(x) = C₁f₁(x) + C₂f₂(x) + c3f3(x) olve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞o, co). If a nontrivial solution exists, state it. (If only the trivial solution exist =1² C2, C3} = {1,8,8 x } etermine whether f₁, f₂, f3 are linearly independent on the interval (-0, ∞o). Olinearly dependent

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 following functions. f₁(x) = x₁ F₂(x) = x², f3(x) = 4x - 2x² g(x) = c₁f₁(x) + C₂f₂(x) + c3f3(x) Solve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {C₁, C₂, C3} = -1.8.8 } X Determine whether f₁, f2, f3 are linearly independent on the interval (-∞, 00). Olinearly dependent O linearly independent
Transcribed Image Text:Consider the following functions. f₁(x) = x₁ F₂(x) = x², f3(x) = 4x - 2x² g(x) = c₁f₁(x) + C₂f₂(x) + c3f3(x) Solve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {C₁, C₂, C3} = -1.8.8 } X Determine whether f₁, f2, f3 are linearly independent on the interval (-∞, 00). Olinearly dependent O linearly independent
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