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.
- MDTERM 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 size of array exceeds 73 columns by 73 rows.
- 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
- 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 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!) |
|
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