# MDETERM function

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.
• MDETERM returns the #VALUE! error when:
• Any cells in array are empty or contain text.
• 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.

Note   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 Formulas tab, in the Formula Auditing group, click the Show Formulas button.
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!)

Applies to:
Excel 2007