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 calcular una matriz inversa 4x4 pero además, te enseñamos cómo se hace el cálculo manualmente a través del determinante 4x4 y la matriz transpuesta de la adjunta.

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 resolver la matriz inversa 4x4 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 a partir del ejemplo que tienes justo encima de estas líneas. No importan las dimensiones que tenga la matriz, por lo que da igual que sea 3x3, 4x4 o nxn, el método de resolución es exactamente el mismo.

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 calcular el determinante 4x4.

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 calcular la matriz adjunta 4x4. 

Basically consists of eliminating the row and column in which each element is located. de la matriz y con los elementos que queden, formar un determinante que tendremos que resolver. Este paso hay que repetirle con todos y cada uno de los elementos que forman la matriz 4x4.

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.

Calcular la matriz inversa 4x4 en Excel

Inverse matrix 4x4

Excel allows you to calcular la matriz inversa 4x4 or any other nxn dimension. To do this, you have to follow the steps below:

  1. Escribe la matriz 4x4 de la cual quieres calcular su inversa
  2. Selecciona un rango 4x4 de celdas vacías para que en ellas se calcule la matriz inversa
  3. A continuación escribe la siguiente fórmula (recuerda tener hecha la selección del rango 4x4):

=MINVERSE(B14:E17)

  1. Una vez escrita la función para calcular la matriz inversa 4x4 en Excel, pulsamos a la vez las teclas Shift (mayúsculas) + CTRL y, sin soltarlas, la tecla INTRO para confirmar la fórmula. Si no pulsamos esas dos teclas, en lugar de aparecer la matriz inversa calculada, saldrá sólo un valor.

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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