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!
Best Answer
Hint: One of the axioms is that $av + bv = (a+b)v$ for scalars $a,b$ and vector $v$. See how that works with your scalar multiplication.