Row Matrix
Row matrix is a matrix having all its elements in a single row. The elements are arranged in a horizontal manner, and the order of a row matrix is 1 x n. A row matrix, A = [a, b, c, d] has only one row and can have numerous columns, which are equal to the number of elements in the row.
Let us learn more about the properties of row matrix, the matrix operations on row matrix, through examples, FAQs.
| 1. | What Is A Row Matrix? |
| 2. | Properties Of Row Matrix |
| 3. | Operations On Row Matrix |
| 4. | Examples on Row Matrix |
| 5. | Practice Questions |
| 6. | FAQs on Row Matrix |
What Is A Row Matrix?
Row matrix is a matrix in which all the elements are in a single row. A row matrix has only one row and multiple columns. The order of a row matrix is 1 × n, and it has n elements.. The elements are arranged in a horizontal manner, with the number of elements equal to the number of columns in a row matrix. The general form of a row matrix is as follows.
A = \(\begin{bmatrix}a_{11}&a_{12}&a_{13}&......&a_{1n}\end{bmatrix}_{1×n}\)
Examples of Row Matrix
Let us look at the below three examples of row matrix.
B = \(\begin{bmatrix}3&2\end{bmatrix}_{1×2}\)
C = \(\begin{bmatrix}a&b&c\end{bmatrix}_{1×3}\)
D = \(\begin{bmatrix}5&7&9&11\end{bmatrix}_{1×4}\)
Properties of Row Matrix
The following properties of the row matrix, help in a deeper understanding of the row matrix.
- A row matrix has only one row.
- A row matrix has numerous columns.
- The number of elements in a row matrix is equal to the number of columns in the matrix.
- A row matrix is also a rectangular matrix.
- The transpose of a row matrix is a column matrix.
- The row matrix can be added or subtracted to only a row matrix of the same order.
- A row matrix can be multiplied with only a column matrix
- The product of a row matrix with a column matrix gives a singleton matrix.
Operations On Row Matrix
The following algebraic operations of addition, subtraction, multiplication, and division can be performed across row matrices. The addition and subtraction operations on row matrices can be performed as for any other matrices. A row matrix can be added or subtracted to any other row matrix only. Here, the order of the two matrices should be the same.
A = \(\begin{bmatrix}3&-5&2&0\end{bmatrix}\), B = \(\begin{bmatrix}5&8&4&7\end{bmatrix}\)
A + B = \(\begin{bmatrix}3+5&(-5)+8&2+4&0+7\end{bmatrix}\) = \(\begin{bmatrix}8&3&6&7\end{bmatrix}\)
The multiplication of a row matrix is possible with a column matrix. Satisfying the condition of matrix multiplication, the number of columns in the row matrix should be equal to the number of rows of a column matrix. That is the number of columns in the first matrix for multiplication should be equal to the number of rows in the second column.
A = \(\begin{bmatrix}4&3&6&-15\end{bmatrix}\), B = \(\begin{bmatrix}6\\5\\4\\2\end{bmatrix}\)
A × B = \(\begin{bmatrix}4×6+3×5+6×4+(-15)×2\end{bmatrix}\) = \(\begin{bmatrix}24+15+24-30\end{bmatrix}\) = \(\begin{bmatrix} 33 \end{bmatrix}\)
The multiplication of a row matrix with a column matrix results in a singleton matrix. Further, the row matrix cannot be used for division, since the inverse of a row matrix does not exist.
Related Topics
The following topics help in a better understanding of row matrix.
FAQs on Row Matrix
What Is A Row Matrix?
A row matrix is a matrix with only one row, and all the elements are arranged one besides the other in a horizontal line. The row matrix A = \(\begin{bmatrix}a&b&c&d\end{bmatrix}\), have the four elements placed in a single column. The row matrix has only one row and numerous columns. The order of a row matrix is 1 × n.
What Is The Order Of Row Matrix?
The order of a row matrix is 1 × n. The row matrix has one row and n number of columns. The number of columns in a row matrix is equal to the number of elements.
What Kind Of A Matrix Is A Row Matrix?
The row matrix is a rectangular matrix. It has an unequal number of rows and columns. The row matrix is equal to have one row and numerous columns based on the number of elements in the matrix.
What Is The Transpose Of A Row Matrix?
The transpose of a row matrix gives a column matrix. The row matrix of order 1 × n, has a transpose matrix, which is a column matrix of order n × 1. The row matrix has elements arranged in a horizontal manner and the column matrix has elements placed in a vertical format.
What Are The Operations Of A Row Matrix?
The matrix operations of addition, subtraction, and multiplication can be performed using a row matrix. The inverse of a row matrix is not possible since it is not a square matrix. The addition or subtraction of matrices is possible between two row matrices of the same order. The multiplication of a row matrix is possible with a column matrix. Satisfying the condition of matrix multiplication, the number of columns in the row matrix should be equal to the number of rows of a column matrix.
What Is the Difference Between Row Matrix And Column Matrix?
The row matrix has elements arranged in a horizontal manner, and the column matrix has elements arranged in a vertical manner. The order of a row matrix is 1 × n, and the order of a column matrix is n × 1. The row matrix or a column matrix has an equal number of elements. And the product of a row matrix and a column matrix results in a singleton matrix.