Definition of linear independence of a vector

Question

The definition of linear independence of a vector.

Let V be a vector space over k. The vector $v_1,v_2,…,v_n ∈ V$ are said to be linearly independent if ∃ scalar $c_1,c_2,…,c_n ∈ K$ not all zero such that $$v_1c_1 + v_2c_2 +… +v_nc_n ≠ 0$$

Is this definition correct about the linear independence of a vector?

Answer 1

No the correct definition is

Let V be a vector space over k. The vector $v_1,v_2,...,v_n \in V$ are said to be linearly independent if $\color{red}{\not \exists}$ scalars $c_1,c_2,...,c_n \in K$ not all zero such that $v_1c_1 + v_2c_2 +... +v_nc_n \color{red}{=0}$