Column matrix

Definition

A column matrix is a matrix with a single column and multiple rows. It is represented as a vertical array of elements.

5 Must Know Facts For Your Next Test

1. A column matrix has the dimension $n \times 1$ where $n$ is the number of rows.
2. It can be used to represent vectors in coordinate geometry.
3. In systems of linear equations, solutions can often be expressed as column matrices.
4. The transpose of a column matrix is a row matrix.
5. Operations like addition, subtraction, and scalar multiplication are easily applied to column matrices.

Review Questions

• What are the dimensions of a column matrix with 5 elements?
• How would you represent the solution to a system of linear equations using a column matrix?
• What happens when you take the transpose of a column matrix?

Related terms

Row Matrix: A row matrix is a matrix with a single row and multiple columns.

Transpose:

The transpose of a matrix is obtained by swapping its rows and columns.

Vector:

In mathematics, especially in linear algebra, a vector can often be represented as either a row or column matrix.