MDETERM

Returns the matrix determinant of an array.

Syntax

MDETERM(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.
• If any cells in array are empty or contain text, MDETERM returns the #VALUE! error value.
• MDETERM also returns #VALUE! if array does not have an equal number of rows and columns.

Remarks

• 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.

Examples

MDETERM({1,3,8,5;1,3,6,1;1,1,1,0;7,3,10,2}) equals 88

MDETERM({3,6,1;1,1,0;3,10,2}) equals 1

MDETERM({3,6;1,1}) equals -3

MDETERM({1,3,8,5;1,3,6,1}) equals #VALUE! because the array does not have an equal number of rows and columns.