I have to prove:(adsbygoogle = window.adsbygoogle || []).push({});

Let [itex]u_{1}[/itex] and [itex]u_{2}[/itex] be nonzero vectors in vector space [itex]U[/itex]. Show that {[itex]u_{1}[/itex],[itex]u_{2}[/itex]} is linearly dependent iff [itex]u_{1}[/itex] is a scalar multiple of [itex]u_{2}[/itex] or vice-versa.

My attempt at a proof:

([itex]\rightarrow[/itex]) Let {[itex]u_{1}[/itex],[itex]u_{2}[/itex]} be linearly dependent. Then, [itex]\alpha_{1}u_{1}+ \alpha_{2}u_{2}=0[/itex] where [itex]\alpha_{1} \not= \alpha_{2} [/itex]...I'm stuck here in this direction

([itex]\leftarrow[/itex]) Fairly trivial. Let and [itex]u_{1} = -u_{2}[/itex]. Then [itex]\alpha_{1}u_{1}+ \alpha_{2}u_{2}=0[/itex] but [itex]\alpha_{1} \not= \alpha_{2} [/itex].

Any ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proving linear dependence

**Physics Forums | Science Articles, Homework Help, Discussion**