Inverse matrix 4×4 online

Do you want to calculate the inverse matrix online? Then you are in the right place.

Below you will find a calculator that will allow you to save you a lot of time when it comes to calculate a 4×4 inverse matrix but in addition, we show you how to do the calculation manually through the 4×4 determinant and the transposed matrix of the adjoint.

When the matrix has no inverse

As you will see in the next point, matrix has no inverse when its determinant is zero.

Therefore, the first thing we must do when it comes to solve the inverse 4×4 matrix consists of solving its determinant, so that if it is null, we have already solved the exercise since we justify that the condition for the matrix to be invertible is not fulfilled.

How to calculate the inverse matrix

Example of a 3x3 matrix

We are going to learn how to calculate the inverse matrix from the example just above these lines. It doesn't matter the dimensions of the matrix, so it doesn't matter if it is 3×3, 4×4 or nxn, the resolution method is exactly the same.

Step 1: Calculate the determinant

3x3 determinant

To calculate the inverse matrix the first thing to do is to calculate its determinant. If you don't know how to do it, here is how to do it calculate the 4×4 determinant.

Once we have the determinant calculated, two things can happen:

  • If its value is 0, the matrix has no inverse.
  • If it is non-zero, the matrix is invertible.

Step 2: Calculate adjoining matrix

Calculation of attachments

The next step consists of calculate the attached 4×4 matrix. 

Basically consists of eliminating the row and column in which each element is located. of the matrix and with the remaining elements, form a determinant that we will have to solve. This step must be repeated with each and every one of the elements that form the 4×4 matrix.

Matrix-4x4-assemblies

And remember that the resulting adjoining matrix must respect the following signs as shown in the figure above. Therefore, the resulting attached matrix will be as follows:

Attached matrix

Step 3: We make the transpose of the adjoining matrix

Matrix transposed from the attached

After having calculated the adjoint matrix, we make its transpose. To do this, we simply exchange rows for columnsso it is very easy to make.

Step 4: Solve the formula for calculating the inverse matrix

Solved example of inverse matrix

The inverse matrix is calculated by multiplying the inverse of the determinant (1/|A|) by the adjoint matrix of the transpose.

Calculating the inverse 4×4 matrix in Excel

Inverse matrix 4x4

Excel allows you to calculate the inverse 4×4 matrix or any other nxn dimension. To do this, you have to follow the steps below:

  1. Write the 4×4 matrix of which you want to calculate its inverse
  2. Selects a 4×4 range of empty cells to calculate the inverse matrix
  3. Then type the following formula (remember to have the 4×4 range selection done):

=MINVERSE(B14:E17)

  1. Once the function to calculate the inverse 4×4 matrix in Excel has been written, press the Shift + CTRL keys and, without releasing them, the ENTER key to confirm the formula. If we do not press these two keys, instead of displaying the calculated inverse matrix, only one value will be displayed.

Note: In the excel function to find the inverse matrixin the parentheses is the range of empty cells that you have selected. In our case we have put the range B14:E17 as an example, but you can use any other.

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