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Excel MDETERM Function

Excel MDETERM function
Summary 

The Excel MDETERM function returns the matrix determinant of a given array. The input array must contain numbers only and be a square matrix, with equal rows and columns. The result is a number representing the matrix determinant.

Purpose 
Get matrix determinant of given array
Return value 
A number representing the matrix determinant
Syntax 
=MDETERM (array)
Arguments 
  • array - A square array of numbers only.
Version 
Usage notes 

The MDETERM function returns the matrix determinant of a given array, which must be a square matrix containing numbers only, and no empty values. In mathematics, the matrix determinant is a scalar value (single value) that is a function of the entries in a square matrix. The determinant is a special number that can help characterize some properties of the matrix. For example, if the determinant is zero, the matrix will not have an inverse.

The MDETERM function takes just one argument, array, which can be provided as a range or an array constant. Array must be a square matrix with the same numbers of rows and columns.

Examples

To get the matrix determinant for the 2 x 2 array shown in B7:C8, the formula in E7 is:

=MDETERM(B7:C8) // returns -1

The equivalent formula with an array constant is:

=MDETERM({4,3;3,2}) // returns -1

To get the matrix determinant for the 3 x 3 array shown in I7:K9, the formula in M7 is:

=MDETERM(I7:K9) // returns 1

The equivalent formula with an array constant is:

=MDETERM({1,0,5;2,1,6;3,4,0}) // returns 1

Notes

  • The array argument must be a square matrix with an equal number of rows and columns
  • The array argument can be provided as a range or array constant like {4,3;3,2}
  • Empty cells or text in array will cause MDETERM to return a #VALUE! error
  • MDETERM returns a #VALUE! if array does not have an equal number of rows and columns

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