Math Help - Bases for R2

1. Bases for R2

Course: Linear Algebra

So I have the set $\left\{(0,0) , (1,3)\right\}$ which I will call S.

I'll have the system:

$c_2 = x_1$
$3c_2 = x_2$

Which gives me $c_2 = x_1 = \frac{1}{3}x_2$

Can this mean that span(S) = R2?
Is the zero vector redundant?

2. Re: Bases for R2

Yes the zero vector is not necessary and you should know that the zero vector is linearly dependent to any other vector since 0*any_vector = 0 vector no matter what vector you use.

3. Re: Bases for R2

Thanks chiro.