Let $W$ be the set of all vectors

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ a $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ b c d

such that a - 2b = 4c and 2a = c + 3d.

Determine if $W$ is a vector space and check the correct answer(s) below.

A. $W$ is not a vector space because it does not have additive closure.
B. $W$ is a vector space because it has a zero element.
C. $W$ is not a vector space because it does not have a zero element.
D. $W$ is a vector space because it can be written as $Nul A$ for some matrix $A$.