2. (LI-1) Compute the Wronskian for each set of functions below and determine whethe the set is linearly independent or linearly dependent. If the set is linearly dependent find constant coefficients for the functions which would make them add up to 0. (a) y₁(x) = x, y₂(x) = x + 10, ys(x) = 2x

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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### Problem 2. (LI-1)

Compute the Wronskian for each set of functions below and determine whether the set is linearly independent or linearly dependent. If the set is linearly dependent, find constant coefficients for the functions which would make them add up to 0.

**(a)**  
\( y_1(x) = x, \quad y_2(x) = x + 10, \quad y_3(x) = 2 - x \)

**(b)**  
\( y_1(x) = x, \quad y_2(x) = x^2 + 4, \quad y_3(x) = x - x^2 \)
Transcribed Image Text:### Problem 2. (LI-1) Compute the Wronskian for each set of functions below and determine whether the set is linearly independent or linearly dependent. If the set is linearly dependent, find constant coefficients for the functions which would make them add up to 0. **(a)** \( y_1(x) = x, \quad y_2(x) = x + 10, \quad y_3(x) = 2 - x \) **(b)** \( y_1(x) = x, \quad y_2(x) = x^2 + 4, \quad y_3(x) = x - x^2 \)
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