This calculator will find the row echelon form of the given matrix with step by step.
Add this calculator to your site
Use this rref calculator that helps you to determine the reduced row echelon form of any matrix by row operations being applied. So stay connected to learn the technique of matrix reduction and how this reduced row echelon form calculator will assist you to amplify your speed of calculations.
A matrix is said to be in either echelon or reduced echelon form if it satisfies the following set of conditions:
Let’s resolve an example to clarify your concept of both echelon and reduced echelon form. Stay focused!
Example:
Find the reduced echelon form of the matrix given below: $$ \begin{bmatrix} 2 & 3 & 8 \\ 14 & 8 & -7 \\ 7 & -3 & 1 \\\end{bmatrix} $$
Solution:
As the given matrix is: $$ \begin{bmatrix} 2 & 3 & 8 \\ 14 & 8 & -7 \\ 7 & -3 & 1 \\\end{bmatrix} $$ Determination of Reduced Echelon Form:
Step # 01:
Divide first row by 2: $$ \begin{bmatrix} 1&\frac{3}{2}&4 \\14&8&-7 \\ 7&-3&1\\\end{bmatrix} $$
Step # 02:
Multiply first row by 14 and subtract it from first row: $$ \begin{bmatrix}1&\frac{3}{2}&4 \\ 0&-13&-63 \\ 7&-3&1 \\\end{bmatrix} $$
Step # 03:
Multiply second row by 7 and minus it from the third row: $$ \begin{bmatrix}1&\frac{3}{2}&4 \\0&-13&-63 \\0&\frac{-27}{2}&-27 \\\end{bmatrix} $$
Step # 04:
Go for dividing the second row by -13: $$ \begin{bmatrix}1&\frac{3}{2}&4 \\0&1&\frac{24230769231}{5000000000} \\0&\frac{-27}{2}&-27 \\\end{bmatrix} $$ We understand that these suppositions in calculations may be confusing but do not worry as this rref calculator
Step # 04:
Now it's time to multiply zeroth row by the number 3/2 and subtract it from first row: $$ \begin{bmatrix}1&0&\frac{-8173076923}{2500000000} \\0&1&\frac{24230769231}{5000000000} \\0&\frac{-27}{2}&-27 \\\end{bmatrix} $$
Step # 05:
Multiply second row by -27/2 and minus it from the third row: $$ \begin{bmatrix}1&0&\frac{-8173076923}{2500000000} \\0&1&\frac{24230769231}{5000000000} \\0&0&\frac{19211538462}{500000000} \\\end{bmatrix} $$
Step # 06:
Move on multiplying third row by 500000000/19211538462: $$ \begin{bmatrix}1&0&\frac{-8173076923}{2500000000} \\0&1&\frac{24230769231}{5000000000} \\0&0&1 \\\end{bmatrix} $$
Step # 07:
Multiply zeroth row by -8173076923/2500000000 and subtract it from first row: $$ \begin{bmatrix}1&0&0 \\0&1&\frac{24230769231}{5000000000} \\0&0&1\\\end{bmatrix} $$
Step # 08:
Get the product of first row with 24230769231/5000000000 and subtract the result from second row as below: $$ \begin{bmatrix}1&0&0 \\0&1&0 \\0&0&1 \\\end{bmatrix} $$ As all principal diagonal elements have zero on above and below them, the form generated is considered a reduced echelon.
This row reduced echelon form calculator will take a couple of moments to generate the row echelon form of any matrix.
Input:
Output:
From the source of wikipedia: Row echelon form, Reduced row echelon form, Transformation, Systems of linear equations, Gaussian elimination, Applications From the source of khan academy: Matrix row operations
Support
Calculator Online Team Privacy Policy Terms of Service Content Disclaimer Advertise TestimonialsEmail us at
[email protected]© Copyrights 2024 by Calculator-Online.net