Let $V =\{(x, y, z, w)|x=y+z, w=2y\}$ be a subspace of $\Bbb{R}^4$.
(i) Write down an explicit form of a general vector of $V$.
(ii) Express $V$ in linear span form.
(iii) Write down a basis for $V$ and find $\dim V$.
To answer (i), I managed to get $\Big\{l(1,0,1,0) + t(1/2,1/2,0,1)|t, l \in \Bbb{R}\Big\}$. Which brings me to the next part (ii) and (iii), is it right to say that both the basis and span of $V$ is
$V= \{(1,0,1,0),(1/2,1/2,0,1)\}$?
Let $y=t,z=s$, then we can then deduce that vectors in $V$ are of this form: $$\Big\{(t+s,t,s,2t)=t(1,1,0,2)+s(1,0,1,0)\;:\;s,t\in \mathbb{R}\Big\}$$ From that the two vectors $(1,1,0,2),(1,0,1,0)$ are linearly independent and form a basis for $V$. So dimension of $V$ is $2$.