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Describing Matrices (Rows and Columns)

In these lessons, we will learn

  • what is a matrix?
  • rows and columns of a matrix
  • dimensions (or order) of a matrix
  • elements of a matrix

Related Topics: Operations on Matrices

A matrix consists of a set of numbers arranged in rows and columns enclosed in brackets.

The dimensions or order of a matrix gives the number of rows followed by the number of columns in a matrix. The order of a matrix with 3 rows and 2 columns is 3 × 2 or 3 by 2.

We usually denote a matrix by a capital letter.

C is a matrix of order 2 × 4 (read as ‘2 by 4’)

Elements In An Array

Each number in the array is called an entry or an element of the matrix. When we need to read out the elements of an array, we read it out row by row.

Each element is defined by its position in the matrix.

In a matrix A, an element in row i and column j is represented by aij


a11 (read as ‘a one one ’)= 2 (first row, first column)

a12 (read as ‘a one two') = 4 (first row, second column)

a13 = 5, a21 = 7, a22 = 8, a23 = 9


Properties of Matrices
The basics of a matrix. Looking at rows, columns, elements and dimension.
This video explains how to determine the dimension of a matrix and why it is important to be able to identify the dimensions of a matrix.

The following video examines how to state the dimensions of a matrix.
Introduction to matrices
What a matrix is. How to add and subtract them.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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