Determine whether the given functions are linearly independent. and x4 e -3x e-3x Choose the correct answer below. O A. The functions are not linearly independent, that is they are linearly dependent, because the equation c₁ f₁ (x) + C₂f₂ (x) + ... + Ckfk (x) = 0 has only the trivial solution. B. The functions are not linearly independent, that is they are linearly dependent, because the second function is a multiple of the first function. OC. The functions are linearly independent because the equation c₁f₁(x) + C₂f₂ (x) + ... + Ck fk (x) = 0 has only the trivial solution. D. The functions are linearly independent because the equation c₁ f₁(x) + C₂f₂(x)+...+ Ckfk (x) = 0 has nontrivial solution(s).

Advanced Engineering Mathematics
10th Edition
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Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Determine whether the given functions are linearly independent.
4 - 3x
and x
e
- 3x
e
Choose the correct answer below.
A. The functions are not linearly independent, that is they are linearly dependent, because the equation c₁f₁ (x) + C₂f₂ (x) + · • + Ckfk (x) = 0 has only the trivial
solution.
B. The functions are not linearly independent, that is they are linearly dependent, because the second function is a multiple of the first function.
C. The functions are linearly independent because the equation c₁f₁ (x) + C₂f₂(x) + ··· + Ck fk (x) = 0 has only the trivial solution.
...
D. The functions are linearly independent because the equation c₁ f₁ (x) + c₂f₂ (x) + ... + Ck fk (x) = 0 has nontrivial solution(s).
Transcribed Image Text:Determine whether the given functions are linearly independent. 4 - 3x and x e - 3x e Choose the correct answer below. A. The functions are not linearly independent, that is they are linearly dependent, because the equation c₁f₁ (x) + C₂f₂ (x) + · • + Ckfk (x) = 0 has only the trivial solution. B. The functions are not linearly independent, that is they are linearly dependent, because the second function is a multiple of the first function. C. The functions are linearly independent because the equation c₁f₁ (x) + C₂f₂(x) + ··· + Ck fk (x) = 0 has only the trivial solution. ... D. The functions are linearly independent because the equation c₁ f₁ (x) + c₂f₂ (x) + ... + Ck fk (x) = 0 has nontrivial solution(s).
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