Question

What is a row matrix ?

Answer 1

Hint: We have to solve this question by stating the definition of row matrix. We will also give examples of row matrices . We will also define the order of the row matrix. We will also mention the various operations of the matrix which can be applied to the row matrix.

Complete answer:
A row matrix is a matrix which has only one row in the matrix . All the elements in a row matrix are arranged in a single row . Such that the matrix has only one and has a number of columns . Hence it is called a row matrix .
The order of a matrix is written in the form of \[n{\text{ }} \times {\text{ }}m\]. For a row matrix the value of \[n{\text{ }} = {\text{ }}1\]. Thus the order of the row matrix is written in the form\[1{\text{ }} \times {\text{ }}m\].
Examples of row matrix are :-
\[\left( i \right)\] \[A{\text{ }} = \left( 1 \right)\]
$A$ is a row matrix of the order \[1{\text{ }} \times {\text{ }}1\] . The matrix has only one element $1$.

\[\left( ii \right)\] $A = [\begin{array}{*{20}{c}}
  1&2
\end{array}]$
$A$ is a row matrix of the order \[1{\text{ }} \times {\text{ }}2\] . The matrix has two elements in a row but in two columns
\[\left( iii \right)\] \[A{\text{ }} = {\text{ [}}\begin{array}{*{20}{c}}
  1&2&3
\end{array}]\]
$A$ is a row matrix of the order \[1{\text{ }} \times {\text{ }}3\] . The matrix has two elements in a row but in three columns
For general the terms of the row matrix are given as \[{A_{(1 \times j)}}\] where $j$ is the number of columns in the matrix .
If the order of the row matrix is \[1{\text{ }} \times {\text{ }}5\] then the elements in the row matrix are at positions \[{A_{(11)}}{\text{ }},{\text{ }}{A_{(12)}}{\text{ }},{\text{ }}{A_{(13)}},{\text{ }}{A_{(14)}}{\text{ }},{\text{ }}{A_{(15)}}{\text{ }}\]

Note: In all the above examples , the elements are arranged in only one row but have different numbers of columns . Similarly , the arrangements of all the elements in the matrix are in the form of a rectangle . Hence , a row matrix is also called a rectangular matrix . Two row matrices having the same order can be added or subtracted using the operations of matrix such that in the sum of two row matrices each element of a row is added to the element of the other matrix in the same position.