Question

Which is the correct coefficient matrix for this system?

Answer 1

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: $AX=B$, 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 $2\times2$ matrix. Our matrices for variable and constant will be of dimensions $2\times1$ (column matrix).

We can represent our given system of equations in matrix form as:

$\left[\begin{array}{ccc}3&4\\-1&-6\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]= \left[\begin{array}{ccc}12\\10\end{array}\right]$

Now let us find our A, X and B parts from above matrices.

$A=\left[\begin{array}{ccc}3&4\\-1&-6\end{array}\right]$

$X=\left[\begin{array}{ccc}x\\y\end{array}\right]$

$B=\left[\begin{array}{ccc}12\\10\end{array}\right]$

Since we know that A represents coefficient matrix, therefore, correct coefficient matrix for our system of equations will be,

$\left[\begin{array}{ccc}3&4\\-1&-6\end{array}\right]$