Let $u=\left[\begin{array}{c}-5\\ -4\end{array}\right],$ and $v=\left[\begin{array}{c}10\\ 5\end{array}\right]$

Select all of the vectors that are in the linear combinations of $\{u,v\}.($Check every statement that is correct.$)$

A$.$ The vector $-5\left[\begin{array}{c}-5\\ -4\end{array}\right]$ is a linear combination of $\{u,v\}.$

B$.$ The vector $\left[\begin{array}{c}10\\ 5\end{array}\right]$ is a linear combination of $\{u,v\}.$

C$.$ The vector $\left[\begin{array}{c}-5\\ -4\end{array}\right]$ is a linear combination of $\{u,v\}.$

D$.$ The vector $\left[\begin{array}{c}0\\ 0\end{array}\right]$ is a linear combination of $\{u,v\}.$

E$.$ All vectors in $R^2$ are linear combinations of the given vectors.

F$.$ The vector $2\left[\begin{array}{c}10\\ 5\end{array}\right]-5\left[\begin{array}{c}-5\\ -4\end{array}\right]$ is a linear combination of $\{u,v\}.$

G$.$ We cannot tell which linear combinations of the given vectors.