Question

Which is the correct coefficient matrix for this system?

3x + 4y = 12

- x - 6y = 10

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*2` matrix. Our matrices for variable and constant will be of dimensions
`2*1` (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]`