Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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## Determining Linear Independence of Functions
Determine whether the given set of functions is linearly independent on the interval \((-\infty, \infty)\).
\[ f_1(x) = 6, \quad f_2(x) = \cos^2(x), \quad f_3(x) = \sin^2(x) \]
- ○ Linearly dependent
- ○ Linearly independent
---
In this exercise, you are asked to determine if the set of functions \( \{ f_1(x), f_2(x), f_3(x) \} \) are linearly independent over the interval \(( -\infty, \infty )\).
Linear independence of functions implies that no function in the set can be written as a linear combination of the others.
To explore more about linear independence of functions, you might want to review the Wronskian determinant and its application in checking independence for functions: [Link to relevant educational material on linear independence].
Ensure that you evaluate the provided functions properly by analyzing their structure and applying the necessary theoretical concepts to determine their linear dependence or independence.
---](https://content.bartleby.com/qna-images/question/0436118d-47b7-4fa9-abd3-dac72bbeccd1/eb41b377-d025-442d-8bea-3dbece645d12/7wkyi3y_processed.jpeg)
Transcribed Image Text:---
## Determining Linear Independence of Functions
Determine whether the given set of functions is linearly independent on the interval \((-\infty, \infty)\).
\[ f_1(x) = 6, \quad f_2(x) = \cos^2(x), \quad f_3(x) = \sin^2(x) \]
- ○ Linearly dependent
- ○ Linearly independent
---
In this exercise, you are asked to determine if the set of functions \( \{ f_1(x), f_2(x), f_3(x) \} \) are linearly independent over the interval \(( -\infty, \infty )\).
Linear independence of functions implies that no function in the set can be written as a linear combination of the others.
To explore more about linear independence of functions, you might want to review the Wronskian determinant and its application in checking independence for functions: [Link to relevant educational material on linear independence].
Ensure that you evaluate the provided functions properly by analyzing their structure and applying the necessary theoretical concepts to determine their linear dependence or independence.
---
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