Mathwords logoMathwords

Row — Definition, Formula & Examples

A row is a horizontal line of entries in a matrix, read from left to right. Rows are counted from top to bottom, so the first row is at the top of the matrix.

In an m×nm \times n matrix AA, the ii-th row is the ordered nn-tuple (ai1,ai2,…,ain)(a_{i1}, a_{i2}, \ldots, a_{in}) for 1≤i≤m1 \leq i \leq m, consisting of all entries whose first subscript index is ii.

Worked Example

Problem: Identify the rows of the matrix and state how many rows it has.
The matrix: Consider the following matrix:
A=[371528]A = \begin{bmatrix} 3 & 7 & 1 \\ 5 & 2 & 8 \end{bmatrix}
Row 1: The first (top) row contains the entries reading left to right:
Row 1=(3,  7,  1)\text{Row 1} = (3,\; 7,\; 1)
Row 2: The second (bottom) row contains:
Row 2=(5,  2,  8)\text{Row 2} = (5,\; 2,\; 8)
Answer: Matrix AA has 2 rows. It is a 2×32 \times 3 matrix (2 rows, 3 columns).

Why It Matters

Rows are essential for describing matrix dimensions, performing row operations in systems of equations, and computing determinants. When you solve a system using Gaussian elimination or Cramer's Rule, every step involves working with individual rows.

Common Mistakes

Mistake: Confusing rows with columns. Some students read down instead of across when identifying a row.
Correction: Rows go horizontally (left to right). Columns go vertically (top to bottom). In the notation m×nm \times n, the first number mm always tells you the number of rows.