Define $(a_1,a_2)+(b_1,b_2)=(a_1+b_1,0)$ and $c(a_1,a_2)=(ca_1,0)$
With these operations, the following conditions
(1)There exists an element in $V$ denoted by $0$ such that $x+0=x$ for each $x$ in $V$
(2) For each element $x$ in $V$ there exists an element $y$ in $V$ such that $x+y=0$
Thus it is not a vector space.
I need more detailed explanation why these two rules do not hold.
Isn't it possible if I put $b_1=-a_1, b_2=-a_2$?