Row Matrix: Definition, Examples, Properties & Operation

A row matrix is a type of matrix between the seven different types of matrices where all the elements are arranged in a single row. A row matrix generally has only one row but can contain numerous columns. Therefore, if the matrix is seen in the order of 1 × n, then it is a row matrix. A row matrix is also known as a row vector. Also, we cannot find the determinant of a row matrix. Only if the number of rows and columns is equal to 1, meaning if the order of the row matrix is 1 × 1, then the determinant of a row matrix can be calculated.

Key Words: Matrix, Row Matrix, Row Vector, Rows, Columns, Horizontal, Rectangle, Column Matrix, Singleton Matrix, Determinant, Horizontal line

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What is a Row Matrix?

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A row matrix is a matrix where all the elements are arranged in a single row. A row matrix can have only one row but it can contain multiple columns. A matrix of an order a × b, where `a’ is the number of rows and `b’ is the number of columns, and the value of `a’ is = 1. Then, a matrix of the order 1 × b is defined as a row matrix.

The elements in a row matrix are arranged in a horizontal manner. Hence, a row matrix is a rectangular array of elements which are arranged in a horizontal line. The mathematical form of a row matrix can be expressed as:

Row Matrix: A=[ a11 a12 a13… a1b ] 1×b

The video below explains this:

Matrices Detailed Video Explanation:

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Examples of Row Matrix

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B=[ 5 6 ] 1×2

C=[ x y z ] 1×3

D=[ 2 1 7 3 ] 1×4

E=[ 4 1 6 3 8 ] 1×5

In these examples, the elements are seen to be arranged in a single row but multiple columns, therefore, all these examples are of row matrices.

Read more: Probability

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Properties of Row Matrix

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The various properties of a row matrix are mentioned below as follows:

• A row matrix has only one row.
• A row matrix contains numerous columns.
• The number of columns in a row matrix is equal to the number of elements in the matrix.
• A row matrix is a rectangular array of elements which are arranged in a horizontal line.
• The transpose of a row matrix is actually a column matrix.
• The addition and subtraction of a row matrix are only possible with a row matrix of the same order.
• The multiplication of a row matrix is only possible with the presence of a column matrix.
• The product of a row matrix with a column matrix actually gives a singleton matrix.

Read more: Logarithms

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Operations of Row Matrix

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The following algebraic operations such as addition, subtraction, multiplication, and division can be performed across row matrices. The addition and subtraction operations on row matrices can be performed similarly to any other matrices. A row matrix can be added or subtracted to another row matrix only. Hence, the order of the two matrices should be the same.

Example of addition:

A= 1 2 5 6 , B=-3 4 2 7

A+B= 1+-3 2+4 5+2 6+7 =[-2 6 7 13]

The multiplication of a row matrix is only possible with the presence of a column matrix. According to the condition of matrix multiplication, the number of columns in the row matrix should be exactly equal to the number of rows of a column matrix. Hence, the number of columns in the first matrix for multiplication should be equal to the number of rows in the second column.

Example of multiplication:

 A= 1 4 3 6 , B= 4271

 A ×B= 1×4+4×2+3×7+6×1

= 4+8+21+6

=[ 39 ]

The multiplication of a row matrix with a column matrix always results in a singleton matrix. Furthermore, the row matrix cannot be used for division, since there is no inverse of a row matrix.

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Things to Remember

• A row matrix is defined as a type of matrix where all the elements present are arranged in a single row.
• A row matrix can have only one row but can contain multiple columns.
• A matrix of the order 1 × n is generally a row matrix.
• A row matrix is a rectangular array of elements where the elements are arranged in a horizontal manner.
• The mathematical form of a row matrix can be expressed as:  A=[ a11 a12 a13… a1n ] 1×n
• The transpose of a row matrix is a column matrix.
• The addition and subtraction of a row matrix are only possible with a row matrix of the same order.
• The multiplication of a row matrix is only possible with the presence of a column matrix.
• The product of a row matrix with a column matrix actually results in a singleton matrix.

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