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Determinant of a matrix

This online calculator computes determinant of a matrix, using it's definition

This page exists due to the efforts of the following people:

Timur

Timur

A

Anton

Created: 2011-06-24 21:29:11, Last updated: 2021-03-03 07:46:50
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This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/1104/. Also, please do not modify any references to the original work (if any) contained in this content.

The site engine now allows input of long texts, so this is the first calculator to use this feature; and it is used to enter the matrix, and the calculator computes the determinant of the entered matrix.

It uses determinant definition, which is a recursive calculation, and, in theory, quite resource consuming. Still, for our case, with matrixes entered manually, I believe it is enough (if not, please use Determinant by Gaussian elimination).

Some notes about determinants are below the calculator for those who forgot.

PLANETCALC, Determinant of a matrix

Determinant of a matrix

Digits after the decimal point: 2
Determinant of a matrix
 

Some recursive formulae:

det A=\begin{vmatrix} a_{11}\end{vmatrix} = a_{11}

  • determinant of a matrix 1x1

det A=\begin{vmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{vmatrix}=a_{11}a_{22}-a_{12}a_{21}

  • determinant of a matrix 2x2

det A=\sum_{j=1}^n (-1)^{1+j} a_{1j}\bar M_j^1

  • determinant of a matrix nxn, where n > 2
    \bar M_j^1 - minor of a_{1j}.
    Minor of a_{1j} - is the determinant of a (n–1) × (n–1) matrix that results from deleting the 1-th row and the j-th column of A. That's why this is a recursive definition.

For example, here is the determinant of a matrix 3x3
det A = \begin{vmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{vmatrix} = a_{11}\begin{vmatrix} a_{22} & a_{23} \\ a_{32} & a_{33} \end{vmatrix}-a_{12}\begin{vmatrix} a_{21} & a_{23} \\ a_{31} & a_{33} \end{vmatrix}+a_{13}\begin{vmatrix} a_{21} & a_{22} \\ a_{31} & a_{32} \end{vmatrix}

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PLANETCALC, Determinant of a matrix
Timur2021-03-03 07:46:50

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