Use the Wronskian to determine if the given functions are linearly independent on the indicated interval. f(x) = 23, g(x) = 6x, h(x) = 4x“; the real line Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer.) O A. The Wronskian W(f, g, h) = As W is never 0 on the real line f(x), g(x) and h(x) are linearly independent. B. The Wronskian W(f, g, h) = As W is identically 0 on the real line f(x), g(x) and h(x) are linearly independent. O C. The Wronskian W(f, g, h) = As W is identically 0 on the real line f(x), g(x) and h(x) are linearly dependent. D. The Wronskian W(f, g, h) = As W is never 0 on the real line f(x), g(x) and h(x) are linearly dependent.
Use the Wronskian to determine if the given functions are linearly independent on the indicated interval. f(x) = 23, g(x) = 6x, h(x) = 4x“; the real line Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer.) O A. The Wronskian W(f, g, h) = As W is never 0 on the real line f(x), g(x) and h(x) are linearly independent. B. The Wronskian W(f, g, h) = As W is identically 0 on the real line f(x), g(x) and h(x) are linearly independent. O C. The Wronskian W(f, g, h) = As W is identically 0 on the real line f(x), g(x) and h(x) are linearly dependent. D. The Wronskian W(f, g, h) = As W is never 0 on the real line f(x), g(x) and h(x) are linearly dependent.
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:Use the Wronskian to determine if the given functions are linearly independent on the indicated interval.
\( f(x) = 23, \, g(x) = 6x, \, h(x) = 4x^2; \) the real line
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Simplify your answer.)
- A. The Wronskian \( W(f, g, h) = \boxed{} \). As \( W \) is never 0 on the real line, \( f(x), g(x) \) and \( h(x) \) are linearly independent.
- B. The Wronskian \( W(f, g, h) = \boxed{} \). As \( W \) is identically 0 on the real line, \( f(x), g(x) \) and \( h(x) \) are linearly independent.
- C. The Wronskian \( W(f, g, h) = \boxed{} \). As \( W \) is identically 0 on the real line, \( f(x), g(x) \) and \( h(x) \) are linearly dependent.
- D. The Wronskian \( W(f, g, h) = \boxed{} \). As \( W \) is never 0 on the real line, \( f(x), g(x) \) and \( h(x) \) are linearly dependent.
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