# Symbolic calculation of 4x4 determinants

## Calculator

The online calculators are to calculate the determinat of 2x2, 3x3, 4x4,... and nxn matrices.

Online Calculators:

## Online Calculator for Determinant 4x4

The online calculator calculates symbolic the value of the determinant of a 4x4 matrix after Sarrus rule and with the Laplace expansion in a row or column.

### Determinant

$\mathrm{det A}=\left|\begin{array}{cccc}{a}_{11}& {a}_{12}& {a}_{13}& {a}_{14}\\ {a}_{21}& {a}_{22}& {a}_{23}& {a}_{24}\\ {a}_{31}& {a}_{32}& {a}_{33}& {a}_{34}\\ {a}_{41}& {a}_{42}& {a}_{43}& {a}_{44}\end{array}\right|$

### Enter the coefficients

Brackets has to be set explicit. Not a+b but (a+b) is ok.

a11= a12= a13= a14=

a21= a22= a23= a24=

a31= a32= a33= a34=

a41= a42= a43= a44=

### Calculation using the Laplace expansion

You can select the row or column to be used for expansion.

### Laplace Expansion Theorem

The Laplacian development theorem provides a method for calculating the determinant, in which the determinant is developed after a row or column. The dimension is reduced and can be reduced further step by step up to a scalar.

$\mathrm{det A}=\sum _{i=1}^{n}{-1}^{i+j}\cdot {a}_{ij}\mathrm{det}{A}_{ij}\text{( Expansion on the j-th column )}$

$\mathrm{det A}=\sum _{j=1}^{n}{-1}^{i+j}\cdot {a}_{ij}\mathrm{det}{A}_{ij}\text{( Expansion on the i-th row )}$

where Aij, the sub-matrix of A, which arises when the i-th row and the j-th column are removed.