Answer
False
Work Step by Step
Let $x=(2a,2b)$ and $y=(2c,2d)$ be vectors in $R^2$ whose components are even integers and $k$ is a scalar
then $x + y=(2a,2b)+(2c,2d)=(2a+2c,2b+2d)=(2(a+b),2(c+d))$ is also a vector whose components are even integers.
$kx$ are also vectors in $R^2$ are said to be even integers if and only if the number $k$ is an integers. In such a situation that $k$ is not an integer, then the components of vector $kx$ are not even integers.
