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
4.8K
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
- 1057 views
- $2.00
Related Questions
- Stuck on this and need the answer for this problem at 6. Thanks
- Let $\mathbb{C} ^{2} $ a complex vector space over $\mathbb{C} $ . Find a complex subspace unidimensional $M$ $\subset \mathbb{C} ^{2} $ such that $\mathbb{C} ^{2} \cap M =\left \{ 0 \right \} $
- Consider the function, prove that it's bilinear, symmetric, and positive definite
- Length of a matrix module
- Find the null space of the matrix $\begin{pmatrix} 1 & 2 & -1 \\ 3 & -3 & 1 \end{pmatrix}$
- Find eigenvalues and eigenvectors of the matrix $\begin{pmatrix} 1 & 6 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 2 \end{pmatrix} $
- Question about interest earned
- Calculate the inverse of a triangular matrix
