Linear Algebra - Show that $V$ is not a vector space Let $V = \{(x,y,z) | x, y, z \in R\}$. Define addition and scalar multiplication on $V$ as follows:
$$(x_1, y_1, z_1) + (x_2, y_2, z_2) = (x_1,y_1+y_2,z_1+z_2)$$
$$c(x_1,y_1) = (2cx_1,cy_1)$$
where $c$ is any real number.
Show that $V$, with respect to these operations of addition and scalar multiplication, is not a vector space by showing that one of the vector space axioms does not hold.
Since I'm new to Linear Algebra, I don't understand how to approach this question, any help would be much appreciated!

Under addition, $V$ should be an abelian group. Especially there should be a neutral element $(x_1,y_1,z_1)$ such that $(x_1,y_1,z_1)+(x_2,y_2,z_2)= (x_2,y_2,z_2)$ for all $(x_2,y_2,z_2)$.
Also, scalar multiplication with $c=1$ should be the identity.
Not to mention that it should be defeined on elements of $V$ in the first place (your definition works with pairs, not triples).
