MDETERM

Returns the matrix determinant of an array.

Syntax

MDETERM(array)

Array is a numeric array with an equal number of rows and columns.

Remarks

Array can be given as a cell range, for example, A1:C3; as an array constant, such as {1,2,3;4,5,6;7,8,9}; or as a name to either of these.
If any cells in array are empty or contain text, MDETERM returns the #VALUE! error value.
MDETERM also returns #VALUE! if array does not have an equal number of rows and columns.
The matrix determinant is a number derived from the values in array. For a three-row, three-column array, A1:C3, the determinant is defined as:
MDETERM(A1:C3) equals
A1*(B2*C3-B3*C2) + A2*(B3*C1-B1*C3) + A3*(B1*C2-B2*C1)
Matrix determinants are generally used for solving systems of mathematical equations that involve several variables.
MDETERM is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the calculation is not complete. For example, the determinant of a singular matrix may differ from zero by 1E-16.

Example

The example may be easier to understand if you copy it to a blank worksheet.

Create a blank workbook or worksheet.
Select the example in the Help topic. Do not select the row or column headers.

Selecting an example from Help
Press CTRL+C.
In the worksheet, select cell A1, and press CTRL+V.
To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.

A	B	C	D
Data	Data	Data	Data
1	3	8	5
1	3	6	1
1	1	1	0
7	3	10	2
Formula	Description (Result)
=MDETERM(A2:D5)	Determinant of the matrix above (88)
=MDETERM({3,6,1;1,1,0;3,10,2})	Determinant of the matrix as an array constant (1)
=MDETERM({3,6;1,1})	Determinant of the matrix in the array constant (-3)
=MDETERM({1,3,8,5;1,3,6,1})	Returns an error because the array does not have an equal number of rows and columns (#VALUE!)