4
$\begingroup$

Under following conditions

$ a, b \in \mathbb{R}, V = \mathbb{R}^{2}, W = \{(x, y)\ |\ ax + by = 0 \} $

is W a subspace of V? I know the basics, but how would I prove that addition and multiplication are closed over this subset?

1 Answers 1

6

Let $(v_1,v_2),(w_1,w_2)\in W.$ We have $\begin{cases} av_1+bv_2=0\\ aw_1+bw_2=0 \end{cases} $ What happens when you add these equations? What happens when you multiply the first equation by a real number $r$?

  • 0
    Yes, of course. Thanks a lot!2012-01-24