Calculate the determinant of a 3×3 matrix online is possible with our calculator. Just fill in the elements that make up the determinant and click on the calculate button to see the result, including the step-by-step method of solving the attached determinants.
We will also teach you how to solving 3×3 determinants by the Sarrus method or using Excel. Read on and you will find all this information and much more.
How to solve 3×3 determinants by Sarrus
The Sarrus rule is a very simple way to calculate the determinant of a 3×3 matrix. This method consists of two parts:
- Sign +: the elements of the diagonal of the determinant and those of the parallel diagonals are multiplied together with their opposite vertex.
- Sign -: the elements of the secondary diagonal are multiplied as well as those of the parallel diagonals taking into account their opposite vertex.
The Sarrus rule for solving 3×3 determinants is a little difficult to understand in theory, so the best thing to do is to look at the image in which we show the order in which the multiplications must be done, both for the positive part and for the part that accompanies the negative sign.
In addition, here is an example of how solving a generic 3×3 determinant by Sarrus:
Obtain determinant of 3×3 matrix by adjuncts
The method of adjoint determinants is another form of solving 3×3 determinants. In this case, you have to choose a row or column of the matrix, preferably with zeros to facilitate the calculations. If there is none that meets this criterion, you can take the one you want.
Now that you have selected a row or column, you need to multiplying each element of the selected line by its adjoining determinant (the one obtained by deleting the row and column in which that element is located). You must also take into account the + or - sign of that element taking into account the following layout:
If you are looking for an example of how to use the attachment method, go to the link we have left you and there you will find one. Even if it is for a 4×4 matrix, the procedure to follow is exactly the same.
Calculate 3×3 determinant in Excel
With Excel you can also calculating a determinant of a 3×3 matrix as you can see in the video we have recorded.
Just open a spreadsheet and write each element of the matrix in an empty cell, respecting its order. When you have filled in all the elements of the matrix in Excel, in the next step, place yourself in an empty cell and type the following function:
Between the parentheses you must write or select the range of cells that your 3×3 matrix occupies in the Excel sheet. In our example in the video, we would write this Excel function for solve the determinant of the matrix:
Undoubtedly, it is a very quick way to check if you have solved the 3×3 determinant well or to save time and avoid possible calculation errors.