Column

Definition

A column in a matrix is a set of elements arranged vertically. Each column represents a variable in systems of linear equations.

5 Must Know Facts For Your Next Test

1. A matrix with $m$ rows and $n$ columns is called an $m \times n$ matrix.
2. The number of columns in the coefficient matrix corresponds to the number of variables in the system of equations.
3. In Gaussian elimination, operations can be performed on entire columns.
4. The identity matrix has ones on the diagonal and zeroes elsewhere, making its columns orthogonal unit vectors.
5. Column operations can affect the solvability and solutions of a system of equations.

Review Questions

• What does each column in a coefficient matrix represent?
• How do you determine the number of columns in an $m \times n$ matrix?
• What effect do elementary column operations have on solving systems of equations?

Related terms

Matrix:

A rectangular array of numbers arranged into rows and columns.

Row: A horizontal set of elements within a matrix that typically represents an equation.

Gaussian Elimination:

A method for solving systems of linear equations by transforming the system's augmented matrix to row-echelon form using row operations.