Problem $6.(1$ point$)$

Note: Throughoutthisquestionyouarerequiredtoworkinmod$2$arithmetic,i$.$e$.,$thefieldF$2=\{0,1\}.$

Consider the matrix

The MATLAB code to produce T is given by:

$$code$$T $=[0,0,0,0,0,0,0,1$;$0,0,0,0,0,1,1,0$;$0,1,0,0,0,1,1,0$;$1,0,0,0,0,0,0,0]/$code$$

Consider each of the following as vectors in F$8.$ Select all the vector$($s$)$ in the solution space of T$.$ If none, $2$

select $$None$.$

$$ A$.$ v$1=(1,0,0,0,0,0,0,0)$ B$.$ v$2=(1,1,0,0,1,0,1,0)$ C$.$ v$3=(0,0,0,0,0,1,0,0)$ D$.$ v$4=(1,0,1,1,1,0,0,0)$ E$.$ v$5=(0,0,1,0,1,0,0,0)$ F$.$ v$6=(0,0,0,0,0,1,0,1)$ G$.$ None