Linear independence of functions
Show that
(i) the functions $f_1(t)=t e^t $ and $f_2(t)=e^t$ are linearly independent on $(0,1)$.
(ii) $f_1(t)=t e^t $ and $f_2(t)=e^t$ are linearly dependent for every fixed $t\in (0,1)$.
I confused about this question. Part (i) and (ii) are really similar, but they are asking me two prove completely different things.
Elviegem
41
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
Erdos
4.7K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 501 views
- $2.00
Related Questions
- two short Linear Algebra questions
- Consider the matrix, calculate a basis of the null space and column space
- Step by step method to solve the following problem: find coordinates of B.
- Hello! I Would like a proof detailed of the following question.
- Find $x$ so that $\begin{bmatrix} 2 & 0 & 10 \\ 0 & x+7 & -3 \\ 0 & 4 & x \end{bmatrix} $ is invertible
- Find the general solution of the system of ODE $X'=\begin{bmatrix} 1 & 3 \\ -3 & 1 \end{bmatrix} X$
- Sum of column spaces
- linear algebra