What is 3x3 3x3 3x3

Determinant 3 × 3

In this article, we'll show you how to use the 3 × 3 determinant compute a matrix. Would you like to be able to determine the 3 × 3 determinant in just a short time? Then take a look at our video.

Determinant 3 × 3 simply explained

The 3 × 3 determinant a matrix , you calculate with the Rule of Sarrus.

You add the products of the elements of the diagonals from top left to bottom right (blue) and subtract the products of the diagonals from bottom left to top right (red).

Example: For the 3 × 3 determinant of the matrix thus arises

.

Note:For the notation of the determinant you can find the spellings or .

Calculate determinant 3 × 3

In order not to have to memorize the above formula, there is a simple method how you can easily remember the calculation of the determinant of a 3 × 3 matrix. Proceed as follows:

First write down the matrix A and note the first two columns of the matrix after it.

Next, look at the entries in the main diagonal

and then you form the product . So you get the first summand of the determinant

.

To find the next two summands of the 3 × 3 determinant, look at the diagonals further to the right.

That is, you add the product first

and then the product

.

Next, look at the secondary diagonal

and pull the product from

.

Do the same with the diagonals next to the secondary diagonal. You pull first from

and then subtract .

In total, the 3 × 3 determinant of A is then given by

.

Note: This approach will Rule of Sarrus called.

example 1

Let's look at an example of this. Let's assume you should 3 × 3 determinant the matrix with the Rule of Sarrus calculate, then you will receive

.

.

Example 2

As the next example we will calculate the 3 × 3 determinant the matrix . You proceed in the same way as in the previous example.

Note: If there are only zeros below the main diagonal, then the 3 × 3 determinant is the product of the elements in the main diagonal.

More topics on the determinant

In addition to the determinant of a 3 × 3 matrix, we have prepared other topics for you that deal with the determinant. Make sure to also check out our videos on the following topics:

Determinant 3 × 3 tasks

In this section you can calculate a 3 × 3 determinant practice by solving the following tasks.

Exercise 1: Determinant of a 3 × 3 matrix

Calculate the 3 × 3 determinant the matrix with the Rule of Sarrus.

Solution to task 1

To compute the 3 × 3 determinant of matrix A, you use Sarrus' rule.

Exercise 2: 3 × 3 determinants

Determine the Determinant of the 3 × 3 matrix.

Solution to task 2

The solution of the 3 × 3 determinant is given by Sarrus' rule

.