# Manuals/calci/DET

DET(array)

• is the set of numbers.

## Description

• This function gives the determinant value of a matrix.
• To calculate the determinant of a matrix, we can choose only square matrix.i.e. Number of rows and number of columns should be equal.
• Determinant of the identity matrix is always 1.
• Determinant of the matrix   is denoted by   or  .
• Let   be 2x2 matrix with the elements

• Then  , where   all are real numbers.
• Let   be the 3x3 matrix with the elements

Then  :

• Let   be a square matrix of order  . Write  ,
• Where   is the entry on the   row and   column and   to   &   to  .
• For any   and  , set   (called the co-factors), then the general formula for determinant of the matrix   is,

, for any fixed  . Also , for any fixed  .

• This function will give the result as error when
1. Any one of the element in array is empty or contain non-numeric
2. Number of rows is not equal to number of columns


## Examples

1. =DET([[6,4,8],[3,6,1],[2,4,5]]) = 104
2. =DET([[-5,10],[6,-8]]) = -20
3. =DET([[1,0,2,1],[4,0,2,-1],[1,4,5,2],[3,1,2,0]]) = 17
4. =DET([1,2,3],[5,2,8]) = NAN

Determinants