# Row of a Matrix

## Definition

The presentation of elements in a horizontal straight path inside a matrix by giving some space between every two elements, is called a row of a matrix.

A row is a horizontal straight path inside a matrix. It holds the elements one after one in the matrix. Each row is separated from another row by some space to separate elements of one row from elements in another row in the matrix.

## Example

$M$ is a matrix and it contains the elements in an order.

$\begin{bmatrix} \begin{array}{|cccc|} \hline 3 & 8 & -5 & 2 \\\hline 20 & -9 & -1 & -5 \\\hline 6 & 13 & 7 & 0 \\\hline \end{array} \end{bmatrix}$

Look at the example matrix and it is formed by the arrangement of four elements in a horizontal straight path and it is called as a row of the matrix. In order to separate the one row from another and also to avoid elements gets mixed, some space is displayed between every two rows of the matrix.

It means,

• $3,8,–5$ and $–2$ are four elements in first row.
• $20,–9,–1$ and $–5$ are four elements in second row.
• $6,13,7$ and $0$ are four elements in third row.

### Representation

A row can be denoted by a letter $R$ and the number of every row is displayed as subscript to the letter $R$. As per the system of set theory, the elements of every row can be written as a set in mathematical form.

• The elements in first row ${R}_{1}=\left\{3,8,–5,–2\right\}$
• The elements in second row ${R}_{2}=\left\{20,–9,–1,–5\right\}$
• The elements in third row ${R}_{3}=\left\{6,13,7,0\right\}$
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