# I Question On Linear Independence

1. Nov 2, 2016

### Cantspel

We were going over linear independents in class and my professor said that if y1 and y2 are linearly independent then the ratio of y2/y1 is not a constant, but he never explained why it is not a constant.

2. Nov 2, 2016

### BvU

Hi,
You can turn it around: if y1 and y2 are linearly dependent, there is a $\lambda$ such that $y_1 = \lambda y_2$

3. Nov 2, 2016

### Krylov

Given that you posted this in a differential equations subforum, I take it that $y_1$ and $y_2$ belong to some vector space of functions that contains the solutions of a certain linear differential equation?

Provided this is indeed your setting, what (by definition) does it mean when $y_{1,2}$ are independent? What does it mean when they are dependent?

4. Nov 2, 2016

### Staff: Mentor

Minor point -- you were going over linear independence in class. Linear independence is an attribute of a set of vectors of other elements that belong to a vector space.