Row

Definition

A row in a matrix is a horizontal grouping of elements. Each row contains a set of values that can represent coefficients in systems of equations.

5 Must Know Facts For Your Next Test

1. Rows are indexed starting from 1 at the top to n at the bottom.
2. In matrix notation, rows are often manipulated using elementary row operations to solve systems of equations.
3. Swapping two rows, multiplying a row by a non-zero scalar, and adding or subtracting multiples of rows are valid elementary row operations.
4. The number of rows in a matrix determines its height but not necessarily its width; this is only defined by the number of columns.
5. Row-echelon form and reduced row-echelon form are specific types of matrices achieved by performing row operations.

Review Questions

• What is the indexing convention for rows in a matrix?
• Name three elementary row operations used in solving systems of equations.
• How does the number of rows affect the dimensions of a matrix?

Related terms

Column: A vertical grouping of elements in a matrix. Columns are analogous to variables when representing systems of equations.

Elementary Row Operations: Operations including swapping rows, multiplying a row by a non-zero scalar, and adding/subtracting multiples of other rows used to simplify matrices.

Row-Echelon Form: A type of form for matrices where each leading entry (the first non-zero number from left) in a row is to the right of the leading entry in the previous row.