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: [tex]AX=B[/tex], 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 [tex]2\times2[/tex] matrix. Our matrices for variable and constant will be of dimensions [tex]2\times1[/tex] (column matrix).
We can represent our given system of equations in matrix form as:
[tex]\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][/tex]
Now let us find our A, X and B parts from above matrices.
[tex]A=\left[\begin{array}{ccc}3&4\\-1&-6\end{array}\right][/tex]
[tex]X=\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]
[tex]B=\left[\begin{array}{ccc}12\\10\end{array}\right][/tex]
Since we know that A represents coefficient matrix, therefore, correct coefficient matrix for our system of equations will be,
[tex]\left[\begin{array}{ccc}3&4\\-1&-6\end{array}\right][/tex]
