How to find all vectors so that a vector equation can be solved? Unfortunately, my text book doesn't clarify this process at all.  It's asking to find all all vectors [a b] so that the vector equation can be solved.  The vector equation is:
$c1$ $[3,1]$ + $c2 [6,2]$=$[a, b]$
The linear system would look like:
$3c1+6c2=a$
$c1+2c2=b$
My text doesn't give any indication how to solve this and I'm stuck.  Any help would be appreciated!  Also, apologies since I can't get the vector forms inserted properly!

Hint: 
You have two equations, and two variables (we treat a, b as constants). Set up the associated augmented coefficient matrix, row reduce, and solve for $c_1, c_2$, which can each be expressed as functions of $a, b$. From that, you should also be able to express $a, b$ as functions of the constants $c_1, c_2$.
Associated augmented coefficient matrix to your system of equations:
$$\begin{pmatrix} 3 & 6 &\mid& a\\ 1 & 2 & \mid & b\end{pmatrix}$$
TIP: Be sure to choose a value for $b$ that will ensure the system is consistent. 
