Math & Trig
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=MDETERM()
Returns the matrix determinant of an array.
Applies To:
Excel for Microsoft 365Excel for Microsoft 365 for MacExcel 2024Excel 2024 for MacExcel 2021Excel 2021 for MacExcel 2019Excel 2016
=MDETERM(array)
Hover argument names in the table for details.
Output typeNumber
Popularity45 / 100
VolatileNo
Dynamic ArrayNo
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◧ Arguments
| Argument | Type | Required | Description |
|---|---|---|---|
array |
Range | Required | A numeric array with an equal number of rows and columns. |
▣ Examples
▦ Data
| Cell | Value |
|---|---|
A2 |
1 |
B2 |
3 |
C2 |
8 |
D2 |
5 |
A3 |
1 |
B3 |
3 |
C3 |
6 |
D3 |
1 |
A4 |
1 |
B4 |
1 |
C4 |
1 |
D4 |
0 |
A5 |
7 |
B5 |
3 |
C5 |
10 |
D5 |
2 |
A6 |
1 |
B6 |
3 |
C6 |
8 |
D6 |
5 |
A7 |
1 |
B7 |
3 |
C7 |
6 |
D7 |
1 |
A8 |
1 |
B8 |
1 |
C8 |
1 |
D8 |
0 |
A9 |
7 |
B9 |
3 |
C9 |
10 |
D9 |
2 |
Determinant of the matrix above
=MDETERM(A2:D5)
Result:
88
Determinant of the matrix as an array constant
=MDETERM({3,6,1;1,1,0;3,10,2})
Result:
1
Determinant of the matrix in the array constant
=MDETERM({3,6;1,1})
Result:
-3
Returns an error because the array does not have an equal number of rows and columns.
=MDETERM({1,3,8,5;1,3,6,1})
Result:
#VALUE!
§ 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.
✦ Tips
- 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.
- 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.
⚠ Common Errors
#VALUE!
MDETERM returns the #VALUE! error when: Any cells in array are empty or contain text.
Fix: Use a square numeric array
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