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3x-2y=4

-6x+4y=7

solve with inversion method

Guest May 5, 2015

Best Answer 

 #3
avatar+19632 
+10

Inverse Matrix Method

Example:

Inverse Matrix Method

Step 1: Rewrite the system using matrix multiplication:

Inverse Matrix Method

and writing the coefficient matrix as A, we have

Inverse Matrix Method example.

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

Solving system of equations

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

Inverse Matrix Method.

On the right, you get

Inverse Matrix Method solution

and so the solution is

Inverse Matrix Method example

heureka  May 6, 2015
 #1
avatar+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
avatar+92781 
0

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

Is that the common term for matix solutions?

Melody  May 6, 2015
 #3
avatar+19632 
+10
Best Answer

Inverse Matrix Method

Example:

Inverse Matrix Method

Step 1: Rewrite the system using matrix multiplication:

Inverse Matrix Method

and writing the coefficient matrix as A, we have

Inverse Matrix Method example.

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

Solving system of equations

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

Inverse Matrix Method.

On the right, you get

Inverse Matrix Method solution

and so the solution is

Inverse Matrix Method example

heureka  May 6, 2015
 #4
avatar+92781 
0

Thank you Heureka  

Melody  May 6, 2015

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