In mathematics, there are four basic operations on numbers namely addition, subtraction, multiplication and division. But in matrices,there are only three operation that we can apply on rows of a given matrix:

- Interchanging the two rows like $R_{1}\leftrightarrow R_{2}$
- Multiply any row by a scalar or number $3R_{1}$ or $4R_{2}$
- Multiply k times the elements of a row. Then, add and subtract p times the corresponding elements of another row, where k and p are real numbers.

These operations are called Elementary Row Transformation

*. *We can easily understand these operations from the examples shown below:

Let A = $\begin{bmatrix}

2 &1 &3 &7 \\

2 &6 &4 &8 \\

1 &1 &0 &1

\end{bmatrix}$

Apply the following operation on matrix A, $R_{1}\leftrightarrow R_{3}$ (interchanging the rows)

B $\approx $ $\begin{bmatrix}

1 &1 &0 &1 \\

2 &6 &4 &8 \\

2 &1 &3 &7

\end{bmatrix}$

Apply the following operation on matrix B, $R_{2}\rightarrow$$\frac{1}{2}\times R_{2}$ (multiplying row by a number)

C $\approx $ $\begin{bmatrix}

1 &1 &0 &1 \\

1 &3 &2 &4 \\

2 &1 &3 &7

\end{bmatrix}$

Apply the following operation on matrix C, $R_{3}\rightarrow R_{3}-2R_{2}$ (operation between two rows)

D $\approx $ $\begin{bmatrix}

1 &1 &0 &1 \\

1 &3 &2 &4 \\

0 &-5 &-1 &-1

\end{bmatrix}$

Thus, after applying Elementary Transformation on A, we have obtained the matrix D.