# Linear independence of functions

(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