To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)
Top

Gauss Jordan Elimination Calculator
Top
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

Back to Top
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

Back to Top
  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


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



    Answer  :  

    X = -1, y = 2 and z = 3



*AP and SAT are registered trademarks of the College Board.