Statement: If $v_1 = 2v_1-3v_2 + 2v_3$ then $\{v_1, v_2, v_3\}$ is a linearly dependent amount.
My question: Is this statement true or not?
My answer: I guess it is linearly dependent amount due to that
$$v_1 = 2v_1-3v_2 + 2v_3\Rightarrow v_1-3v_2+2v_3=0$$ which is linearly dependent if $c_1v_1 +c_2v_2 +\ldots+c_pv_p =0$ if $c_i$ isn't equal to zero.
Am I thinking correct?