Let $W$ be the set of all vectors

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ b - 2d $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 5bd + d b + 3d d

where b and d are real.

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

A. $W$ is a vector space because it can be expressed as $W=Span \{ v_{1},...,v_{n} \}$.
B. $W$ is a vector space because it can be written as $Nul A$ for some matrix $A$.
C. $W$ is not a vector space because it does not have a zero element.
D. $W$ is not a vector space because it does not have additive closure.