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

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3x-2y=4

-6x+4y=7

solve with inversion method

Guest May 5, 2015

#3
+19632
+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
+19632
+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
+92781
0

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

Is that the common term for matix solutions?

Melody  May 6, 2015
#3
+19632
+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
#4
+92781
0

Thank you Heureka

Melody  May 6, 2015