A matrix is a rectangular arrangement of elements i.e numbers into m rows and n columns. The order of that particular matrix is defined as m x n. Row matrix is a type of matrix where the number of rows is always equal to one. Go through the complete article to know the useful details like definition, examples, properties and operations of row matrix.
What is a Row Matrix?
A row matrix is a matrix that has only one row. A matrix of an order m x n, where m is the number of rows, n is the number of columns is said to be a row matrix if and only if, m = 1. Mathematically, a row matrix can be expressed as \( A =\left[
\begin{matrix}
a11 & a12 & a13 & . . . & a1n\cr
\end{matrix}
\right]
\)
The order of the row matrix is 1 x n and n is the number of elements in it. It is not a square matrix so it is not possible to find the determinant of it. The horizontal lines of elements form a row matrix. Read the below sections to know more important details about the single row matrix.
Examples of Row Matrix
Some of the examples of the row matrix are given here.
\(\left[\begin{matrix}
5\cr
\end{matrix}
\right]
\)
- The order of above matrix is 1 x 1
\begin{matrix}
1 & 6\cr
\end{matrix}
\right]
\)
- The order of above matrix is 1 x 2
\begin{matrix}
7 & 2 & 3\cr
\end{matrix}
\right]
\)
- The order of above matrix is 1 x 3
\begin{matrix}
10 & 9 & 8 & 7\cr
\end{matrix}
\right]
\)
- The order of above matrix is 1 x 4
\begin{matrix}
10 & 20 & 30 & 40 &50\cr
\end{matrix}
\right]
\)
- The order of above matrix is 1 x 5.
Row Matrix – Properties
Below given properties of the row matrix are helpful for a better understanding of this matrix.
- It has only one row.
- It can have any number of columns.
- It is also a rectangular matrix.
- The number of elements in a row matrix is equal to the number of columns in it.
- The transpose of a row matrix is a column matrix.
- A row matrix can be multiplied only by a column matrix.
- The row matrix can be added to or subtracted from a row matrix of the same order.
- The product of a row matrix and a column matrix gives the singleton matrix as the product.
Operations on Row Matrix
The algebraic operations such as addition, subtraction, multiplication can be performed on two or more row matrices.
Row Matrices Addition and Subtraction:
To perform an addition or subtraction operation, two matrices must have the same order. The elements of the first matrix are added to or subtracted from the respective elements of the second matrix in case of addition or subtraction.
Examples:
\( A =\left[
\begin{matrix}
12 & 11 & 35\cr
\end{matrix}
\right]
\), \( B =\left[
\begin{matrix}
3 & 4 & 9\cr
\end{matrix}
\right]
\)
\(A + B =\left[
\begin{matrix}
12 + 3 & 11 + 4 & 35 + 9\cr
\end{matrix}
\right]
\) = \(\left[
\begin{matrix}
15 & 15 & 44\cr
\end{matrix}
\right]
\)
\(A – B =\left[
\begin{matrix}
12 – 3 & 11 – 4 & 35 – 9\cr
\end{matrix}
\right]
\) = \(\left[
\begin{matrix}
9 & 7 & 26\cr
\end{matrix}
\right]
\)
Multiplication of Row Matrix:
Multiplication of row matrices is possible only with a column matrix and the product is a singleton matrix.
Example:
\( A =\left[
\begin{matrix}
6 & 5 & 1\cr
\end{matrix}
\right]
\), \( B =\left[
\begin{matrix}
3\cr
4\cr
2\cr
\end{matrix}
\right]
\)
\( A x B =\left[
\begin{matrix}
3 x 6 + 4 x 5 + 1 x 2\cr
\end{matrix}
\right]
\) = \(\left[
\begin{matrix}
40\cr
\end{matrix}
\right]
\)
Questions on Row Matrix
Question 1:
Find the size of the matrix \( A =\left[
\begin{matrix}
2 & 1 & 5 & 6 & 8 & 13 & 42\cr
\end{matrix}
\right]
\)
Solution:
The order of the matrix \( A =\left[
\begin{matrix}
2 & 1 & 5 & 6 & 8 & 13 & 42\cr
\end{matrix}
\right]
\) is 1 x 7 and it has 7 elements in it.
Question 2:
Find the transpose of \(\left[
\begin{matrix}
5 & 6 & 1 & 8 & 10\cr
\end{matrix}
\right]
\)
Solution:
The transpose of a row matrix is a column matrix.
The transpose of a given matrix is \(\left[
\begin{matrix}
5\cr
6\cr
1\cr
8\cr
10\cr
\end{matrix}
\right]
\)
Question 3:
Get the sum and difference of the following matrices.
\( A =\left[
\begin{matrix}
9 & 7 & 3 & 2 & 2 & 1 & 6\cr
\end{matrix}
\right]
\), \( B =\left[
\begin{matrix}
1 & 7 & 10 & 5 & 2 & 3 & 4\cr
\end{matrix}
\right]
\)
Solution:
Given matrices are \( A =\left[
\begin{matrix}
9 & 7 & 3 & 2 & 2 & 1 & 6\cr
\end{matrix}
\right]
\), \( B =\left[
\begin{matrix}
1 & 7 & 10 & 5 & 2 & 3 & 4\cr
\end{matrix}
\right]
\)
\( A + B =\left[
\begin{matrix}
9 + 1 & 7 + 7 & 3 + 10 & 2 + 5 & 2 + 2 & 1 + 3 & 6 + 4\cr
\end{matrix}
\right]
\) = \(\left[
\begin{matrix}
10 & 14 & 13 & 7 & 4 & 4 & 10\cr
\end{matrix}
\right]
\)
\( A – B =\left[
\begin{matrix}
9 – 1 & 7 – 7 & 3 – 10 & 2 – 5 & 2 – 2 & 1 – 3 & 6 – 4\cr
\end{matrix}
\right]
\) = \(\left[
\begin{matrix}
8 & 0 & -7 & -3 & 0 & -2 & 2\cr
\end{matrix}
\right]
\)
Frequently Asked Questions
1. What is row matrix and example?
A row matrix is a matrix that has only one row. The example is \(\left[
\begin{matrix}
5 & 8 & 15 & 10\cr
\end{matrix}
\right]
\).
2. What is row matrix order?
The row matrix order depends on the number of columns or elements it has because the number of rows is always equal to 1. The general row matrix order is 1 x n. Where n is the number of elements in a row matrix.
3. What is the difference between row and column matrices?
In a row matrix, the elements are arranged in a horizontal manner. The column matrix has elements arranged in a vertical manner. The order of a column matrix is n x 1 and the row matrix is 1 x n. The product of a row and column matrix results in a singleton matrix.
4. What is the transpose of a row matrix?
The transpose of a row matrix is a column matrix. The row matrix of order 1 x n is transposed into a column matrix of order n x 1.