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?
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