# Singular Matrix: Definition, Properties & Example

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• 0:02 Definition of a Matrix
• 1:01 Operations with Matrices
• 3:13 Inverse of a Matrix
• 4:58 Definition of a…
• 5:36 Lesson Summary

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Lesson Transcript
Instructor: Beverly Maitland-Frett

Beverly has taught mathematics at the high school level and has a doctorate in teaching and learning.

The use of a matrix is a very old mathematics practice. This lesson will define the singular matrix, but before we can dive into the concept of this matrix, we'll need to discuss some important basics.

## Definition of a Matrix

A matrix is the method of using columns and rows to display or write a set of numbers. The plural form for the word matrix is matrices. A matrix is identified first by its rows, and then by its columns. For example, we say a 'two by two matrix,' but we'd write it in the form '2 x 2.' This means that this matrix has two rows and two columns. There can be different combinations of matrices, such as 3 x 2 or 3 x 1, depending on what's being worked on. Let's take a look at some examples.

## Operations with Matrices

We can only add and subtract matrices that have the same number of rows and columns. Likewise, we only add or subtract the numbers that are in the same position.

In the case of multiplication, we multiply row by column. Therefore, we can only multiply two matrices if the number of rows in the first matrix is the same as the column in the second. In this example, we'll multiply a 3 x 2 matrix by a 2 x 3 matrix. The resulting matrix will be a 3 x 3 matrix.

To do this, we multiply row by column: the first row by the first column, the first row by the second column, and the first row by the third column. Then, we do the same for the second and third row. Multiplying matrices is simple, but can be very tedious. You'll get better at it and be more accurate with practice.

## Inverse of a Matrix

Just as the inverse of 2 is 1/2, a 2 x 2 matrix has an inverse. In this lesson, we'll only find the inverse of a 2 x 2 matrix, though they all have one. In order to find the inverse of a 2 x 2 matrix, there are some steps that we need to follow:

1. Find the determinant:

The symbol for determinant is like the absolute value sign where the letter is written between two vertical lines, like this:

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