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Gauss Jordan Elimination Calculator
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Gauss Jordon Elimination Calculator calculates the value of  Variables in the given matrix.
Consider the matrix to be of the form $AX$ = $B$

$\begin{bmatrix} a_{1} x & b_{1} y & c_{1} z\\ a_{2} x & b_{2} y & c_{2} z\\ a_{3} x & b_{3} y & c_{3} z\\ \end{bmatrix}$ = $\begin{bmatrix} b_{1}\\ b_{2}\\ b_{3}\end{bmatrix}$

The Method operated here is the matrix $A$ is converted into Identity matrix to get the values of $x, y, z$.

## Steps for Gauss Jordan Elimination Calculator

Step 1 :

Write the given matrix in the form of augmented matrix A

Step 2 :

Using Elementary row operation for matrix A such that leading 1s colums have only 0s in the colums other than the leading ones

Step 3 :

The row operations should be reduced to get echelon form which gives the answer.

## Problems on Gauss Jordan Elimination Calculator

1. ### Solve the Problem by Gauss Jordon method:x + 2y = 3-x -2z = -5-3x -5y + z = -4

Step 1 :

Take first row as R1, second row as R2 and third row as R3.

$\begin{bmatrix} 1 & 2 & 0 & | 3 \\ -1 & 0 & -2 & | -5 \\ -3 & -5 & 1 & | -4 \end{bmatrix}$

Step 2 :

Using operations R2 ~ R2 + R1

R3 ~ R3 + 3R1

$\begin{bmatrix} 1 & 2 & 0 & | 3 \\ 0 & 2 & -2 & | -2 \\ 0& 1 & 1 & | 5 \end{bmatrix}$

Operating R1 ~ R1 - R2 and R2 = $\frac{R_{2}}{2}$

$\begin{bmatrix} 1 & 0 & 2 & | 5 \\ 0 & 1 & -1 & | -1 \\ 0 & 1 & 1 & | 5 \end{bmatrix}$

Operating R3 ~ R3 - R2

$\begin{bmatrix} 1 & 0 & 2 & | 5 \\ 0 & 1 & -1 & | -1 \\ 0 & 0 & 2 & | 6 \end{bmatrix}$

Operating R3 ~ $\frac{R_{3}}{2}$

$\begin{bmatrix} 1 & 0 & 2 & | 5 \\ 0 & 1 & -1 & | -1 \\ 0 & 0 & 1 & | 3 \end{bmatrix}$

Step 3 :

Operating R1 ~ R1 - 2R3 and R2 ~ R2 +R3

$\begin{bmatrix} 1 & 0 & 0 & | -1 \\ 0 & 1 & 0 & | 2 \\ 0 & 0 & 1 & | 3 \end{bmatrix}$