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 spreadsheet.

Create a blank spreadsheet.
Select the example in the Help topic.

Selecting an example from Help
Press CTRL+C.
In the spreadsheet, select cell A1, and press CTRL+V.
To switch between viewing the formula that returns the result and the result in the cell, select the cell and press F2 and then ENTER, or click Commands and Options on the spreadsheet toolbar, click the Formula tab, and look in the Formula in active cell (active cell) box.

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!)