We have been given a system of equations and we are asked to write correct coefficient matrix for this system. 
Since we know that a matrix for a system of equations is in the form:  , where A represents the coefficient matrix, X is variables''s matrix and B is the constant matrix.
, where A represents the coefficient matrix, X is variables''s matrix and B is the constant matrix.           
We are given two equation and two unknown variables, so our coefficient matrix will be a  matrix. Our matrices for variable and constant will be of dimensions
 matrix. Our matrices for variable and constant will be of dimensions  (column matrix).
 (column matrix). 
We can represent our given system of equations in matrix form as:
![\left[\begin{array}{ccc}3&4\\-1&-6\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]= \left[\begin{array}{ccc}12\\10\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%264%5C%5C-1%26-6%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%5C%5C10%5Cend%7Barray%7D%5Cright%5D)
Now let us find our A, X and B parts from above matrices. 
![A=\left[\begin{array}{ccc}3&4\\-1&-6\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%264%5C%5C-1%26-6%5Cend%7Barray%7D%5Cright%5D)
![X=\left[\begin{array}{ccc}x\\y\end{array}\right]](https://tex.z-dn.net/?f=X%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D)
![B=\left[\begin{array}{ccc}12\\10\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%5C%5C10%5Cend%7Barray%7D%5Cright%5D)
 Since we know that A represents coefficient matrix, therefore, correct coefficient matrix for our system of equations will be,
![\left[\begin{array}{ccc}3&4\\-1&-6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%264%5C%5C-1%26-6%5Cend%7Barray%7D%5Cright%5D)