Question

PLEASE HELP ME

Which is the correct coefficient matrix for this system?

3x - 4y = 12

x + 6y = 10

Answer 1

As per the matrix theory the given system of equations can be written as:

`AX=B`....................(Equation 1)

Where, A is the Coefficient Matrix (always a square matrix),

X is the variables' matrix (always a column matrix), and

B is the Constant Matrix (again always a column Matrix).

Since our's is a two system equation in two unknowns, we will have the coefficient matrix as a 2x2 square matrix and the other two matrices will be 2x1 column matrices.

Thus, the given system in terms of matrices will be:

`\begin{bmatrix}3 &-4 \\ 1 & 6\end{bmatrix}\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}12\\ 10\end{bmatrix}`

Comparing the above equation with (Equation 1) we can clearly see that the correct coefficient matrix of the given system is:

`A=\begin{bmatrix}3 &-4 \\ 1 & 6\end{bmatrix}`