# If $v_1 = 2v_1-3v_2 + 2v_3$ then ${v_1, v_2, v_3}$ is a linearly dependent amount.

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?

• Yes. the vectors depend each other. – hamam_Abdallah Dec 13 '18 at 14:08
• Thanks for your help – J.Andreasson Dec 13 '18 at 14:12