Could someone please explain why, if two vectors in a set of three are parallel to each other, that this implies that the whole set of three vectors is linearly dependent? I have tried to show this algebraically and to understand it graphically but I simply cannot see how one implies the other.

  • 1
    $\begingroup$ Consider the (mathematical) condition for two vectors to be parallel. Then compare it to the condition that they are dependent. You'll see ... $\endgroup$ – Matti P. Apr 17 at 8:07

The vectors would be, say, $\mathbf v$, $k\mathbf v$ and $\mathbf w$. Then $$k\mathbf{v}+(-1)k\mathbf{v}+0\cdot\mathbf{w}=\mathbf{0}$$

  • $\begingroup$ Thanks very much $\endgroup$ – user193203821309 Apr 17 at 8:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.