What does row mean in math?

A row in general means a horizontal arrangement of objects or things. What does rows mean in math? In math as well, the term “row“ has a similar meaning. It usually refers to the horizontal arrangements of numbers. Such numbers can be in the form of lists or a matrix. Let us understand the inference of this term with respect to both lists and matrices.

Row as a list of numbers

We know that a list of numbers in math is an arrangement of numbers separated by commas. For instance, a list of even natural numbers is usually written as 2, 4, 6, 8, 10, . . . . and so on. The numbers when written in such an arrangement where they are listed in order from left to right, are what we call being arranged in a row. Hence, a row in terms of a list of numbers is simply writing the numbers separated by a comma. Let us take an example.

Example

What will be the set of numbers who set builder form is as below –

A = { x ∈ N, x ≤ 8 and x ≫ 20 }

Solution

We have been given a set A that is defined as –

A = { x ∈ N, x ≤ 8 and x ≫ 20 }

In order to find the numbers that will be contained in this set, we first need to understand what is given to us. Set A contains a number, say x which is a natural number. Also this number, x is greater than or equal to 8 and less than or equal to 20. Now, we know that natural numbers are the counting numbers that start from 1 and go on up to infinity.

By this definition, the numbers that should fall in set A should be the numbers greater than or equal to 8 and less than or equal to 20. Therefore, the numbers would be 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20. Hence, the arrangement of numbers of the set A would be

A = { 8, , 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

We can see above that the numbers have been listed in the order in a horizontal manner. This is what is termed a row of numbers in math.

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What is a row in a table?

A table of numbers in math is a representation of numbers in a horizontal and vertical manner. The horizontal lines are called rows while the vertical lines are called columns. Let us consider an example.

Example

Suppose we have the following table –

Now, the numbers 1 , 2, 3, 4 and 5 form one row of this table. Similarly, the numbers, 1, 6, 11, 16 and 21 form one column. So, we can say that there are 5 rows in the above table, namely,

The first row consists of the numbers -1, 2, 3, 4, 5

The second row consists of the numbers – 6, 7, 8, 9, 10

The third row consists of the numbers – 11, 12, 13, 14, 15

The fourth row consists of the numbers – 16, 17, 18, 19, 20

The fifth row consists of the numbers – 21, 22, 23, 24, 25 

Similarly, there are 5 columns in this table, namely

The first column consists of the numbers – 1, 6, 11, 16, 21

The second column consists of the numbers – 2, 7, 12, 17, 22

The third column consists of the numbers – 3, 8, 13, 18, 23

The fourth column consists of the numbers – 4, 9, 14, 9, 24

The fifth column consists of the numbers – 5, 10, 15, 20, 25

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What is a row in a matrix?

The term row is of major significance in understanding the concept of matrices in math. A matrix in math is an arrangement of numbers in rows and columns. The general form of a 3 x 3 matrix is given by

If we observe the above matrix carefully, we can see that there are three rows and three columns in this matrix.  Such a matrix having 3 rows and 3 columns is called a 3 x 3 matrix.

There are different types of matrices depending upon the number of rows in a matrix. Let us learn about some of them

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Row Matrix

A matrix that has only one row is called a row matrix. For example, consider the following matrix –

A = [ 1    4    5   – 6 ]

The above matrix A has a single row while there are 4 columns in this matrix. Such a matrix is known as a row matrix.

Column Matrix

Similarly, if a matrix has just one column and “ n  “ number of rows, it is called a column matrix. For example, let us consider the following matrix

The above matrix has 5 rows and a single column. Hence it is known as a column matrix.

Let us now understand how to perform various operations in matrices depending on the number of rows and columns. But, before that, we must understand what we mean by Equality of matrices

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Equality of Matrices

Two matrices, A and B are said to be equal if and only if –

• The number of rows in both matrices is equal. This means that if there are “ n “ number of rows in A, then in matrix B as well there are exactly “ n “ number of rows.
• The number of columns in both matrices is equal. This means that if there are “ n “ number of columns in A, then in matrix B as well there are exactly “ n “ number of columns.
• The respective values in the matrices are equal.

Let us consider an example.

Let us understand the addition/subtraction of matrices depending upon their number of rows.

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Addition and Subtraction of Matrices

In order to add or subtract two matrices, it is important to check their order. The order of a matrix means the number of rows and columns present in the matrix. This means that if a matrix is of the order m x n, then the number of rows in the matrix is “ m “ and the number of columns in the matrix is “ n “. So, we can say that the order of the matrix means the number of rows of the matrix followed by the number of columns.

Now, addition or subtraction between matrices can be performed only if the two matrices involved have the same order. Let us consider an example.

Example

Find the sum of the matrices A and B where –

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And we need to find their sum.

Now, to add two matrices, we need to add the value of each position in matrix A with the corresponding position in matrix B. This means that the value at a_11 in matrix A will be added to the value at a_11 in matrix B. This means that

Similarly, we can perform subtraction in matrices. Let us now understand the multiplication of matrices with respect to the number of rows.

Multiplication of Matrices

Let us understand the multiplication of a row matrix and a column matrix. We know that a row matrix of order 1 x 3 can be defined as

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What does rows mean in math: FAQs