Describe all vectors v in R^2 w/ span{v}={(x,y) | 2x+3y=0}

[DarkSun]

I need a direction with the following question:

Describe all vectors v in R^2 such that span{v}={(x,y) | 2x+3y=0}

I don't really understand what does it mean...

 

[DrMike]

The 'span' of a set of vectors means 'all possible linear combinations' of the set.

So the 'span' of v is {av:a in R}

You are asked : find all v=(t,u) such that {(at,au):a in R} = {(x,y):2x+3y=0}.

Does that help?

 

[DarkSun]

yes, thanks alot.

 

[pka]

\(\displaystyle 2x+3y=0\) is a line in \(\displaystyle R^2\). As such it is a one dimensional subspace of \(\displaystyle R^2\).
It is the one dimensional subspace \(\displaystyle \left\{ {\left( {t,\frac{{ - 2}}{3}t} \right):t \in \Re } \right\}\).

 

[DrMike]

Thanks, pka