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There are various ways to arrange numbers and symbols for ease of calculation or convenience in mathematics. The matrix is one of such arrangements. A matrix is a rectangular arrangement or array of numbers and symbols which is used for the representation of a mathematical object or its property. There are various types of matrices, such as the triangular matrix, diagonal matrix, row matrix, column matrix, etc. A matrix having a single row is called the row matrix. A row matrix can have multiple columns. Let us study in-depth about such a row matrix.
Matrices
A matrix is a table containing rows and columns in a particular arrangement. Matrices are of various types. The arrangement of matrices helps make performing operations on them convenient. The square matrices are the most common types of matrices to be found. A square matrix has as many numbers of rows as there are columns.
Matrices are widely used in geometry in order to represent coordinate changes and geometric transformations. There are various types of matrices based on their specific properties. Let’s take a look at what a row matrix is.
Row matrix
The matrix which only has 1 row in it is called the row matrix. Suppose the order of the matrix is m into n, then for a row matrix, the value of m is equal to 1.
An example of a row matrix is:
The above row matrix has a single row, and the total number of elements is 2.
Another row matrix example is given below.
Here, the Matrix also has a single row, and the total number of elements is 3.
You may have noticed that the total number of elements in a row matrix is equal to the number of columns in a row matrix. Let us study the properties of a row matrix.
The properties of a row matrix
The following are the important properties of the row matrix that help us understand the row matrix better.
A row matrix can only contain a single row.
A row matrix contains any number of columns.
A row matrix is a rectangular type of matrix. That means the number of columns here is not equal to the number of rows here generally unless it’s a 1×1 matrix.
The total number of elements in a row matrix is equal to the total number of columns present in a row matrix.
Suppose we want to perform addition or subtraction to a row matrix, then only another row matrix of the same order can be used for addition or subtraction with the row matrix.
The multiplication of a row matrix can only be performed with the column matrix.
After the multiplication of a raw Matrix with a column matrix, we get a singleton matrix as a product.
The order of a row matrix
The order of a matrix indicates the number of rows and columns present in a matrix. Since the row matrix, by definition, will always contain a single row, the order of the row matrix will be 1 × n. The value of m will always stay one for the row matrix.
The number of columns differs, and it is represented by n. The n could take any positive integer values like 2, 5, 9, etc.
Transpose of a row matrix
Before learning what a transpose of a row matrix is, let us learn what is meant by the transpose of a matrix.
The transfers of a matrix are one of the operators used on the matrix. In transpose, the matrix is flipped over from its diagonals. That is, the row and column indices of a matrix are flipped. Let us see what a transpose of a row matrix is. Let us take the matrix given below as an example.
The above matrix has one row and three columns.
So, according to the rules of transposition, the rows of a matrix should become columns, and the columns should become rows.
Hence, the transpose of the above row matrix is given below.
The transpose of the row matrix with one row and three columns is a matrix with one column and four rows.
Conclusion:
A matrix is a rectangular or tabular way to arrange a number of symbols. A matrix represents mathematical objects or properties of mathematical objects. Various operations can also be performed on these matrices. There are various types of matrices like a square matrix, a rectangular matrix, a row matrix, etc. The row matrix is a type of matrix that only contains a single row and any number of columns. It is a rectangular type of matrix. The transpose of a row matrix is a column matrix. A row matrix can only be multiplied by a column matrix.
