A straight horizontal path in a matrix to arrange the elements in the same path is called a row of a matrix.

The space inside the matrix is divided into number of rows according to following two factors.

- The total number of elements.
- The arrangement of number of elements equally in each row.

In every row, the elements are arranged in horizontally straight path but separated by some space.

It can be expressed in general form matrix form as follows.

$ \begin{bmatrix} \begin{array}{|ccccc|} \hline e_{11} & e_{12} & e_{13} & \cdots & e_{1n} \\\hline e_{21} & e_{22} & e_{23} & \cdots & e_{2n} \\\hline e_{31} & e_{32} & e_{33} & \cdots & e_{3n} \\\hline \vdots & \vdots & \vdots & \ddots & \vdots \\\hline e_{m1} & e_{m2} & e_{m3} & \cdots & e_{mn} \\\hline \end{array} \end{bmatrix} $

The total number elements is $mn$. So, the space inside the matrix is divided into $m$ rows to place $n$ elements in each row.

Observe each element closely. Each element displays two numbers in its subscript position. The first number is common to each element in every row because it represents the number of that row.

For example, the number in subscript position of each element in first row is $1$ and it is common to all the elements in that row. The number $1$ represents the element belongs to first row and this rule is same for all the rows.

The general form matrix is simply written in compact form.

$ \begin{bmatrix} e_{\displaystyle ij} \end{bmatrix} $

The element $e_{\displaystyle ij}$ represents every element in the matrix and the first letter $i$ in subscript position of the element represents the number of the respective element’s row.

Observe the following example matrices to understand the concept of row in matrix much better.

$ \begin{bmatrix} \begin{array}{|c|} \hline 6 \\\hline \end{array} \end{bmatrix} $

There is only one element in this matrix. So, it is placed in row and therefore the element $e_{11} = 6$.

$ \begin{bmatrix} \begin{array}{|cccc|} \hline 0 & 2 & 4 & 7 \\\hline \end{array} \end{bmatrix} $

The matrix has only one row but contains four elements. So, $e_{11} = 0$, $e_{12} = 2$, $e_{13} = 4$ and $e_{14} = 7$.

$ \begin{bmatrix} \begin{array}{|cc|} \hline -1 & 9 \\\hline 5 & 8 \\\hline 2 & -5 \\\hline \end{array} \end{bmatrix} $

This matrix has three rows and two elements are placed in each row. Therefore, $e_{11} = -1$, $e_{12} = 9$, $e_{21} = 5$, $e_{22} = 8$, $e_{31} = 2$ and $e_{32} = -5$.

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

This matrix has four rows and four elements are placed in each row. So, $e_{11} = 3$, $e_{12} = 8$, $e_{13} = -5$, $e_{14} = 2$, $e_{21} = 20$, $e_{22} = -9$, $e_{23} = -1$, $e_{24} = -5$, $e_{31} = 6$, $e_{32} = 13$, $e_{33} = 7$, $e_{34} = 0$, $e_{41} = 5$, $e_{42} = -2$, $e_{43} = -6$ and $e_{44} = 3$.

List of most recently solved mathematics problems.

Jun 22, 2018

Integral Calculus

Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

Jun 21, 2018

Limit

Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

Jun 20, 2018

Differentiation

Learn how to find derivative of $\sin{(x^2)}$ with respect to $x$.

Jun 19, 2018

Limit (Calculus)

Find $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{x-\sin{x}}{x^3}$

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.