How to use RREF Calculator?

This Reduced Row Echelon Form Calculator transforms the input matrix to reduced row echelon form.

To use this calculator:

1. Select the Matrix Dimension, The first input is for rows and second is for column.
2. Enter the matrix values in the input fields provided.
3. Click on the calculate button
4. The calculator will display the reduced row echelon form step by step, and the final result.

What is Reduced Row Echelon Form?

Reduced Row Echelon Form (RREF) is a matrix obtained by applying row operations to a matrix until it satisfies the following conditions:

1. Main Diagonal elements are 1.
2. All elements except diagonal are 0.

How to achieve Row Echelon Form?

To achieve row echelon form, we have to perform row operation on matrix.

1. Row Interchange: Interchange two rows of the matrix.
2. Row Scaling: Multiply a row by a non-zero scalar.
3. Row Replacement: Replace a row by the sum of that row and a multiple of another row.

Steps for Row Echelon Form Example

Let's take an example of a matrix and convert it to row echelon form.

Given Matrix:

Equation 1: 3x + 4y = 21
Equation 2: 4x + 8y = 32

The above equation in matrix form is:

\(M = \begin{bmatrix}
3 & 4 & 21 \\
4 & 8 & 32 \\
\end{bmatrix}

\)

Step 1: Divide Row 1 by 3 (R1 = R1/3)

\(M = \begin{bmatrix}
1 & \frac{4}{3} & 7 \\
4 & 8 & 32 \\
\end{bmatrix}
\)

Step 2: Subtract 4 times Row 1 from Row 2 (R2 = R2 - 4R1)

\(M = \begin{bmatrix}
1 & \frac{4}{3} & 7 \\
0 & 4 & 4 \\
\end{bmatrix}
\)

Step 3: Divide Row 2 by 4 (R2 = R2/4)

\(M = \begin{bmatrix}
1 & \frac{4}{3} & 7 \\
0 & 1 & 1 \\
\end{bmatrix}
\)

Step 4: Subtract 4/3 times Row 2 from Row 1 (R1 = R1 - 4/3 R2)

\(M = \begin{bmatrix}
1 & 0 & 5 \\
0 & 1 & 1 \\
\end{bmatrix}
\)

Any Error or Suggestion?

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