MDETERM function: Description, Usage, Syntax, Examples and Explanation
What is MDETERM function in Excel?
MDETERM function is one of the Math and Trig functions in Microsoft Excel that returns the matrix determinant of an array.
Syntax of MDETERM function
MDETERM(array)
The MDETERM function syntax has the following arguments:
- Array: A numeric array with an equal number of rows and columns.
MDETERM formula explanation
- 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 of MDETERM function
Steps to follow:
1. Open a new Excel worksheet.
2. Copy data in the following table below and paste it in cell A1
Note: For formulas to show results, select them, press F2 key on your keyboard and then press Enter.
You can adjust the column widths to see all the data, if need be.
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! |