## Simplest and shortest Matrix method to solve linear equations of 3 variables

# Matrix method to solve linear equations of 3 variables

In this post we are going to understand the concept of solving linear equations of three variables with the help of matrix method .

Matrix method to solve linear equations of three variables with the help of example.

**X = A**-------> (*)

^{-1}B**Evaluation of Determinant**

## How to calculate co factors of all the elements of the matrix A

## i. e. Co factors of 1st row are 14, -6 , -6

Co factors of 2nd row are -(0 -24), (12 - 18) , -(16 - 0) I. e. Co factors of 2nd row are 24 , -6 , -16

Co factors of 3rd row are (0 - 36), -(4 - 18), (24 - 0) i.e. Co factors of 3rd row are -36 , 14 , 24

## Co factor Matrix

## Adjoint Matrix

## Inverse Matrix

^{ }

**A**in (4) After simplification and using the properties of equality of two matrices ( Two matrices of same order are equal iff their respective elements are equal to each other )

^{-1}**⇒**x = 10