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#3**+10 **## 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

heureka May 6, 2015

#1**+5 **

**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

heureka May 5, 2015

#2**0 **

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

Is that the common term for matix solutions?

Melody May 6, 2015

#3**+10 **

Best Answer## 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

heureka May 6, 2015