Linearly Independent Vectors

Assume have three vectors, $v_1$ , $v_2$ , $v_3$ :

Can we express one vector as a linear combination of the other two? If yes, then the vectors are Linearly Dependent.

Linear Combination

In the example below, $v_1$ is a linear combination of $v_2$ and $v_3$ .

$v_1 = a_2v_2 + a_3v_3$ where $a_2$ and $a_3$ are scalars. For this formula, it is allowable for one, but not both, of $a_2$ and $a3$ to be zero.

$v_1 = 2 v_2$

A set of vectors is Linearly Independent if no vector is a linear combination of the other vectors.