Consider the following functions. f₁(x) = x, f₂(x) = x², f3(x) = 6x - 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} = Determine whether f₁, f2, f3 are linearly independent on the interval (-∞, ∞). O linearly dependent O linearly independent
Consider the following functions. f₁(x) = x, f₂(x) = x², f3(x) = 6x - 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} = Determine whether f₁, f2, f3 are linearly independent on the interval (-∞, ∞). O linearly dependent O linearly independent
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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Transcribed Image Text:Consider the following functions.
f₁(x) = x, f₂(x) = x², f3(x) = 6x - 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} =
Determine whether f₁, f2, f3 are linearly independent on the interval (-∞, ∞).
O linearly dependent
O linearly independent
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