1. What Is a Row Matrix?
A row matrix is a matrix that has only one row and any number of columns. It is the simplest type of matrix because the entire matrix lies in a single horizontal line.
If a matrix has order 1 × n, then it is a row matrix.
In general, a row matrix looks like:
\( A = [a_{11} \; a_{12} \; a_{13} \; \cdots \; a_{1n}] \)
2. Understanding the Structure of a Row Matrix
Because it has only one row, all elements of a row matrix lie in the first row. There is no second row, third row or anything below it. Each entry is simply placed next to the other horizontally.
2.1. Example of a Row Matrix
Here is a typical row matrix:
\( R = \begin{bmatrix} 5 & -3 & 0 & 8 \end{bmatrix} \)
This matrix has:
- 1 row
- 4 columns
So its order is 1 × 4, which makes it a row matrix.
2.2. More Examples
- \( [7 \; 2] \) is a row matrix of order \( 1 \times 2 \).
- \( [-4 \; 0 \; 6 \; 9] \) is a row matrix of order \( 1 \times 4 \).
- \( [1] \) is also a row matrix (order \( 1 \times 1 \)), although it is just a single number.
3. How to Identify a Row Matrix
To quickly recognise whether a given matrix is a row matrix, ask yourself:
- Does the matrix have only one horizontal row?
- Are all elements written in the same row without anything below?
If both answers are yes, it is a row matrix.
4. Why Row Matrices Matter
Row matrices appear often while solving systems of linear equations, representing data points, or simplifying matrix operations. They are especially helpful when:
- writing coefficients of a single linear equation,
- displaying a single set of values,
- working with vector-like quantities in matrix form.
Understanding row matrices makes it easier to study vectors, transpose, and matrix multiplication later.