Computing the span 
Compute the span of $\begin{bmatrix} 4\\2\\10 \end{bmatrix}$ and $\begin{bmatrix} 6\\3\\15 \end{bmatrix}$

I just don't even understand what "Compute the span" is even asking me. Can anyone give me a similar example so I can mimic it?
 A: Hint $$\begin{bmatrix} 4\\2\\10 \end{bmatrix}  = \frac{2}{3}\begin{bmatrix} 6\\3\\15 \end{bmatrix}$$
EDIT: Since $\begin{bmatrix} 4\\2\\10 \end{bmatrix} and\begin{bmatrix} 6\\3\\15 \end{bmatrix}$ are linearly dependent, by the definition of span:
For all $\lambda$, $\mu \in R$
The span of these vector is  $\lambda\begin{bmatrix} 4\\2\\10 \end{bmatrix}+ \mu \begin{bmatrix} 6\\3\\15 \end{bmatrix}$ = $\lambda\begin{bmatrix} 4\\2\\10 \end{bmatrix}+ \frac{2\mu}{3} \begin{bmatrix} 4\\2\\10 \end{bmatrix}$ = $(\lambda+ \frac{2\mu}{3} )\begin{bmatrix} 4\\2\\10 \end{bmatrix}$
Let U = $(\lambda+ \frac{2\mu}{3} ) \in R$ so the span {U$\times\begin{bmatrix} 4\\2\\10 \end{bmatrix}$}
A: Meaning of Span of two vectors is all possible vectors made by the those basis vectors. Eg. let $v=span\{ v_1,v_2\}$, then $v=c_1v_1+c_2v_2$ where $c_1,c_2$ are Real no's. But while spanning two or more vectors, make sure that they should be linealy independent.
In your case, span{ $
        \begin{bmatrix}
        4 \\
        2 \\
        10 \\
        \end{bmatrix},
\begin{bmatrix}
        6 \\
        3 \\
        15 \\
        \end{bmatrix}
$} = $c$$\begin{bmatrix}
        2 \\
        1 \\
        5 \\
        \end{bmatrix} $ , where $c$ is any real number
You can clearly see that both of the vectors can be formed using the third vector. By putting $c=2$, you will get first vector and $c=3$, you will get second. This is the final answer.
May be, this can help you in understanding the span.
