Let ${\bf u} = \left[{\begin{matrix}2 \cr 5 \cr \end{matrix}}\right]$, and ${\bf v} = \left[{\begin{matrix}4 \cr 12 \cr \end{matrix}}\right]$.

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

A. The vector $4 \left[{\begin{matrix}4 \cr 12 \cr \end{matrix}}\right]+ 5 \left[{\begin{matrix}2 \cr 5 \cr \end{matrix}}\right]\ $ is a linear combination of $\lbrace {\bf u}, {\bf v} \rbrace$.
B. The vector $5\left[{\begin{matrix}2 \cr 5 \cr \end{matrix}}\right]$ is a linear combination of $\lbrace {\bf u}, {\bf v} \rbrace$.
C. All vectors in ${\mathbb R}^2$ are linear combinations of the given vectors.
D. The vector $\left[{\begin{matrix}4 \cr 12 \cr \end{matrix}}\right]$ is a linear combination of $\lbrace {\bf u}, {\bf v} \rbrace$.
E. The vector $\left[{\begin{matrix}2 \cr 5 \cr \end{matrix}}\right]$ is a linear combination of $\lbrace {\bf u}, {\bf v} \rbrace$.
F. The vector $\left[{\begin{matrix}0 \cr 0 \cr \end{matrix}}\right]$ is a linear combination of $\lbrace {\bf u}, {\bf v} \rbrace$.
G. We cannot tell which linear combinations of the given vectors.