Determine which of the following pairs of functions are linearly independent. ✓ 1. f(0) = cos(30) g(0) = 5 cos³ (0) – 5 cos(0) 2. f(t) = e^t cos(µt) g(t) = et sin(ut)‚μ‡0 3. f(x) = x³ 4. f(t) = 3t, Linearly dependent Linearly dependent Linearly independent Linearly independent " " " g(x) = |x|³ g(t) = |t|
Determine which of the following pairs of functions are linearly independent. ✓ 1. f(0) = cos(30) g(0) = 5 cos³ (0) – 5 cos(0) 2. f(t) = e^t cos(µt) g(t) = et sin(ut)‚μ‡0 3. f(x) = x³ 4. f(t) = 3t, Linearly dependent Linearly dependent Linearly independent Linearly independent " " " g(x) = |x|³ g(t) = |t|
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:Determine which of the following pairs of functions are linearly independent.
Linearly dependent ✓ 1. f(0) = cos(30) g(0) = 5 cos³ (0) — 5 cos(0)
Linearly dependent ✓ 2. f(t) = e¹t cos(µt) g(t) = e^t sin(µt),μ‡0
Linearly independent
3. f(x) = x³, g(x) = |x|³
Linearly independent
4. f(t) = 3t
2
2
9
g(t) = |t|
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