MDETERM function

This article describes the formula syntax and usage of the MDETERM function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Excel.

Description

Returns the matrix determinant of an array.

Syntax

`MDETERM(array)`

The MDETERM function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• Array    Required. 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.

1. Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
Important: Do not select the row or column headers.

Selecting an example from Help

1. Press CTRL+C.
2. Create a blank workbook or worksheet.
3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
Important: For the example to work properly, you must paste it into cell A1 of the worksheet.
4. 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.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

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 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses