Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {e - 9x 6x e on (-00,00) 1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The functions are linearly dependent because c₁ e (Type integers or simplified fractions.) B. The functions are linearly independent because c₁ e ... 9x + c₂e + C3 ex=0 has the solution C₁ = C₂ = and c3 = -1. - 9x + C₂ ex + C3 e* = 0 has no solutions for constants C₁, C₂, and c3 that are not all zero.
Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {e - 9x 6x e on (-00,00) 1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The functions are linearly dependent because c₁ e (Type integers or simplified fractions.) B. The functions are linearly independent because c₁ e ... 9x + c₂e + C3 ex=0 has the solution C₁ = C₂ = and c3 = -1. - 9x + C₂ ex + C3 e* = 0 has no solutions for constants C₁, C₂, and c3 that are not all zero.
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:Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.
- 9x 6x
{e
ex) on (-00,00)
e
1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- 9x
O A. The functions are linearly dependent because c₁ e
(Type integers or simplified fractions.)
6x
+ C₂ e + C3 ex=0 has the solution C₁ =
-9x
OB. The functions are linearly independent because c₁ e
6x
x+c₂e²
...
*+C3 ex
C2 =
and c3 = -1.
= 0 has no solutions for constants C₁, C₂, and c3 that are not all zero.
1.
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