MDETERM function

Returns the matrix determinant of an array.



Array     is a numeric array with an equal number of rows and columns.


  • 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.


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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 2007