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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 following diagram shows the rows and columns of a 3 by 2 matrix. Scroll down the page for more examples and solutions.

matrix row column example

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.
A matrix is a rectangular arrangement composed of row, columns and elements.
The dimensions of the matrix are determined by the number of rows and columns.
What are the dimensions of the matrix below?

We can use a matrix to represent points, or a polygon.When we do this
• The x-coordinates are the first row.
• The y-coordinates are in the second row.
• Each point is a column.
What is the matrix for the following triangle?
How to determine the dimension of a matrix and why it is important to be able to identify the dimensions of a matrix?
A matrix is a rectangular arrangement or array of numbers often called eleents.
The size or dimensions m × n of a matrix identifies how many rows and columns a specific matrix has. The number of rows is m and the number of columns is n.

1. The dimension of a matrix must be known to identify a specific element in the matrix.
2. To add matrices, the dimensions must be the same.
3. To multiply matrices the number of columns in the first matrix must be the same number of rows in the second matrix.
How to state the dimensions of a matrix? Introduction to matrices
What a matrix is?
How to add and subtract them?

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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