3x-2y=4 -6+4y=7 solve with inversion method

Inverse Matrix Method

Example:

Step 1: Rewrite the system using matrix multiplication:

and writing the coefficient matrix as A, we have

.

Step 2: FInd the inverse of the coefficient matrix A. In this case the inverse is

Step 3: Multiply both sides of the equation (that you wrote in step #1) by the matrix A-1.

On the left you'll get

.

On the right, you get

and so the solution is

3x-2y=4

-6x+4y=7 solve with inversion method

$$\small{\text{
$
A = \begin{pmatrix} 3 & -2 \\ -6 &4 \end{pmatrix} \qquad
det ~ A = \begin{vmatrix} 3& -2 \\ -6& 4 \end{vmatrix}=3 \cdot 4 -(-6)\cdot (-2) = 12 - 12 = 0
$}}$$

det A = 0, no solution

I have never heard this called 'inversion method' before.

Is that the common term for matix solutions?

Thank you Heureka