The Excel MDETERM Function

Determinant of a Matrix

The Determinant of a square matrix is a measure of scale.

For the following 2x2 and 3x3 matrices: The determinant of the 2x2 matrix, A, is :

and the determinant of the 3x3 matrix, B, is:

det(B) = a(ei - fh) + b(fg - di) + c(dh - eg)
Further details of the Matrix Determinant are given on the Wikipedia Determinant Page

Function Description

The Excel Mdeterm function calculates the determinant of a square matrix.

The syntax of the function is:

MDETERM( array )

where the array argument is an array of numeric values, that represent a square matrix (i.e. has the same number of rows as columns).

Mdeterm Function Examples

The examples below show the Excel Mdeterm function, used to calculate the determinant of a 2x2 and a 3x3 matrix.

Example 1 - 2x2 Matrix

AB
152
271

The above spreadsheet on the right shows a simple 2x2 matrix. The determinant of this matrix can be calculated using the Excel Mdeterm function as follows:

=MDETERM( A1:B2 )

This gives the result -9.

Example 2 - 3x3 Matrix

ABC
1642
2353
3234

The determinant of the simple 3x3 matrix aboveon the right can be calculated using the following Excel Mdeterm function:

=MDETERM( A1:C3 )

This gives the result 40.

For further details and examples of the Excel Mdeterm function, see the Microsoft Office website.

Mdeterm Function Error

If you get an error from the Excel Mdeterm Function, this is likely to be the #VALUE! error:

Common Error
 #VALUE! - Occurs if either:The supplied matrix contains blanks or non-numeric values;The supplied matrix has unequal numbers of rows and columns.