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?

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

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