Solve the determinant of a 4×4 matrix online with our calculator and learn how it is calculated using one of the following methods.
If you want to calculate online the determinant of a 4×4 matrixJust fill in the values in our calculator and press the calculate button to get the result you are looking for:
How to calculate the determinant of a 4×4 matrix by adjuncts
A very simple way to calculating the determinant of a 4×4 matrix consists of using the attachment method. This method consists of:
- Choose a row or column of the 4×4 matrix that has as many zeros as possible. In case there is none that meets this requirement, you can choose any row or column.
- Once we have the row selected, we multiply each element of the line by its adjoining determinantthat is, the determinant that we obtain by eliminating the row and column to which that element belongs. In addition, the result of each attached determinant will be accompanied by the corresponding + or - sign according to the position it occupies in the matrix and taking into account the following placement:
Example of determinant of 4×4 matrix by adjuncts
If the explanation is not very clear, we are going to see below a example of a 4×4 determinant solved by the adjoint method.
As we said before, the first thing we are going to do is to choose a row or column. As there are none with zeros, let's choose the first column taking into account the + and - signs that will accompany each element:
Now we have to extract the adjoint determinants of each element (eliminating the row and column to which that element of the 4×4 matrix belongs) and solve each resulting 3×3 determinant:
This method is valid for solving determinants of larger size and although it is a bit laborious because of the number of operations to be performed, it is simple to execute once you know the mechanics of the attachment method.
Sarrus method for calculating a 4×4 matrix
The Sarrus rule serves to calculate a 3×3 determinant but cannot be applied for 4×4 determinants.
Extracting the determinant of a 4×4 matrix in Excel
Excel can help you calculating the determinant of a 4×4 matrix. To do this, the first thing to do is to open a new spreadsheet and write in it the elements of the matrix, each one in a different cell.
When you have the determinant 4×4 In Excel, choose an empty cell and write the following formula in it:
Between the parentheses you must write the range of cells in which the determinant is located. For example, if you have occupied the range A1:D4, the formula should be written like this:
Next, you will see that Excel automatically calculates for you the result of the 4×4 determinant you have written.
If you have any doubts about how to do it, we recommend you to watch the video we have recorded and in which we demonstrate how to do it. how to calculate the determinant of the 4×4 matrix with Excel.