Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {e 4x, e-9x e -*) on (-∞0,00) (...) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 4x - 9x OA. The functions are linearly dependent because C₁ + C₂ e -X=0 has the solution C₁, C₂, and c3 = -1. + C3 e (Type integers or simplified fractions.) 4x e B. The functions are linearly independent because c₁ e -X=0 has no solutions for constants C₁, C₂, and c3 that are not all zero e + C₂ - 9x e + C3
Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {e 4x, e-9x e -*) on (-∞0,00) (...) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 4x - 9x OA. The functions are linearly dependent because C₁ + C₂ e -X=0 has the solution C₁, C₂, and c3 = -1. + C3 e (Type integers or simplified fractions.) 4x e B. The functions are linearly independent because c₁ e -X=0 has no solutions for constants C₁, C₂, and c3 that are not all zero e + C₂ - 9x e + C3
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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Differential equations
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Transcribed Image Text:Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.
{e 4x, e-9x
e-x) on (-00,00)
(...)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
4x
- 9x
+ C₂ e
+ C3 e
-X=0 has the solution C₁, C₂, and c3 = -1.
OA. The functions are linearly dependent because c₁ e
(Type integers or simplified fractions.)
4x
B. The functions are linearly independent because c₁ e
e
-X=0 has no solutions for constants C₁, C₂, and c3 that are not all zero.
+ C₂
- 9x
e
+ C3
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