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.

• 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.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

   Note Do not select the row or column headers.

   Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. 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.

See also:

• Math and trigonometry functions
• MINVERSE
• MMULT
• TRANSPOSE