Row Matrix

In mathematics, a row matrix is a type of matrix that has a single row. But the number of columns could be more than one. Therefore, if the matrix is in the order of 1 x n, then it is a row matrix. The elements are arranged in an order such that they represent a single row in the matrix. On the other hand, unlike the row matrix, a column matrix will have a single column. Learn to determine the order of matrices at BYJU’S.

[bij]1 x n is a Row matrix

A row matrix is not a square matrix, therefore, we cannot find the determinant of such a matrix. Only if the number of rows and columns are equal to 1, means the order of the row matrix 1 x 1, then we can calculate the determinant. Let us learn more about row matrices with examples at BYJU’S.

Types of Matrices

There are majorly seven different types of matrices. They are:

  1. Row matrix
  2. Column matrix
  3. Square matrix
  4. Diagonal matrix
  5. Scalar matrix
  6. Identity matrix
  7. Zero matrix

Definition of Row Matrix

A matrix of an order m x n, where m is the number of rows and n is the number of columns, is a row matrix, if and only if, m = 1. Hence, a matrix of the order of 1 x n is a row matrix. The horizontal lines of elements form a row matrix.

A Row matrix is a rectangular array of elements, ordered in a horizontal line. A row matrix can be expressed in mathematical form as:

\(Row ~Matrix, A=\left[\begin{array}{lllll} b_{11} & b_{12} & b_{13} & \cdots & b_{1 n} \end{array}\right]_{1 \times n}\)

Or in general;

Row matrix = [bij]1xn

Let us see some examples of Row matrices.

Matrix Related Articles

Examples of Row matrix

Example 1: A Row matrix of the order 1 x 1, is:

A = [91×1]

Since, there is only one element in the matrix that is ordered in one row and one column, therefore the determinant of the matrix A is:

Determinant = 9

Example 2: A Row matrix of the order 1 x 2, is:

\(A=\left[\begin{array}{lllll} 1 & 2 \end{array}\right]_{1 \times 2}\)

There are two elements arranged in a single row and two columns in the matrix, hence it is an example of a row matrix.

Example 3: A Row matrix of the order 1 x 3, is:

\(A=\left[\begin{array}{lllll} 1 & 3 & 8 \end{array}\right]_{1 \times 3}\)

In the above example, there are three elements in the matrix arranged in a single row and three columns.

Example 4: A Row matrix of the order 1 x 4, is:

\(A=\left[\begin{array}{lllll} 3 & 4 & 7 & 1 \end{array}\right]_{1 \times 4}\)

The elements in the above example are arranged horizontally, in a single row and four columns.

Example 5: An Row matrix of the order 1 x 5, is:

\(A=\left[\begin{array}{lllll} 2 & 1 & 3 & 6 & 7 \end{array}\right]_{1 \times 5}\)

In this example of a row matrix, the elements are arranged in 5 columns and a single row.

Thus, we can see, in the above examples, the elements are arranged in a single row but multiple columns, therefore, all these are Row matrices.

Practice Questions

  1. Give the examples of Row matrix of the orders of:
    1. 1 x 2
    2. 1 x 3
    3. 1 x 4
    4. 1 x 5
    5. 1 x 6
    6. 1 x 7
  2. What is the size of the given matrix?
\(A=\left[\begin{array}{lllll} 9 & 0 & 7 & 1 & 21 \end{array}\right]\)
  1. What is the order of the matrix?
\(A=\left[\begin{array}{lllll} 1 & -3 & 5 \end{array}\right]\)

Frequently Asked Questions on Row Matrix

What is a Row matrix?

A matrix is called a Row matrix, if it has only one row but possibly multiple columns. It is represented by A1 x n, where n is the number of columns.

What is a row in a matrix?

When the elements are arranged in a matrix horizontally, it forms the rows of the matrix. In general , matrix is an arrangement of elements in rows and columns such that [aij]mxn is a matrix where i and j are positions of the elements, m and n are the number of rows and columns, respectively.

What is the order of the Row matrix?

The order of the Row matrix is 1 x n, where m is the number of columns.

What does a row matrix look like?

A row matrix has elements arranged in a single row, thus it looks like a horizontal line.

How does a Row matrix differ from a column matrix?

A Row matrix has a single row whereas a column matrix has a single column.

What is a 2 x 3 matrix?

A 2 x 3 matrix is a matrix where elements are arranged in two rows and three columns.

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