? ? ? ? Determine which of the following pairs of functions are linearly independent. 1. f(x) = x³, g(x) = |x|³ 2. f(t) = 3t² + 21t, g(t) = 3t² - 21t 3. f(x) = x², g(x) = 4|x|² 4. f(x) = e³x, g(x) = ³(x-3)
? ? ? ? Determine which of the following pairs of functions are linearly independent. 1. f(x) = x³, g(x) = |x|³ 2. f(t) = 3t² + 21t, g(t) = 3t² - 21t 3. f(x) = x², g(x) = 4|x|² 4. f(x) = e³x, g(x) = ³(x-3)
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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Determine which of the following pairs of functions are linearly independent.
✓ 1. f(x) = x³, g(x) = |x|³
✓ 2. f(t) = 3t² + 21t,
3. f(x) = x²,
4. f(x) = e³x,
g(t) = 3t² − 21t
g(x) = 4|x|²
g(x) = µ³(x−3)
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