1. Which of the following pairs of functions are linearly independent? Explain your answer. a. sin ar, cos ar (a ‡0) on (-1, 1). b. r, r on (0,1). c. x, x" (m‡n) on (-∞,∞).
1. Which of the following pairs of functions are linearly independent? Explain your answer. a. sin ar, cos ar (a ‡0) on (-1, 1). b. r, r on (0,1). c. x, x" (m‡n) on (-∞,∞).
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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![1. Which of the following pairs of functions are linearly independent? Explain your
answer.
a. sin ar, cos ar (a ‡ 0) on (−1,1).
b. r, r on (0, 1).
c. ïª, xª (m ‡ n) on (-∞,∞).
Show that and r³ are linearly independent on [-1,1] but the Wronskian
W[r³, r³] is equal to zero for all a.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8084a024-ebf9-4fb7-8600-c7fa04d2572b%2F9571e196-95cb-4dbd-9571-cfb393419d84%2Feh53ft9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Which of the following pairs of functions are linearly independent? Explain your
answer.
a. sin ar, cos ar (a ‡ 0) on (−1,1).
b. r, r on (0, 1).
c. ïª, xª (m ‡ n) on (-∞,∞).
Show that and r³ are linearly independent on [-1,1] but the Wronskian
W[r³, r³] is equal to zero for all a.
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