The MDETERM function returns the matrix determinant of an array.

Syntax

=MDETERM(array)

Arguments

Argument Description
array A numeric array with an equal number of rows and columns

Examples

  A B C D E F G
1 Data Data Data   Formula Result Notes
2 6 4 1   =MDETERM(A2:C4) 11 Determinant of the matrix A2:C4 at left
3 3 5 6   =MDETERM(A2:B3) 18 Determinant of the matrix A2:B3 at left
4 2 3 4   =MDETERM({3,6,2;1,1,4;3,10,2}) -40 Determinant of the matrix as an array constant
5         =MDETERM({3,4;1,1}) -1  

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if either:

  the supplied matrix contains blanks or non-numeric values
  the supplied matrix has unequal numbers of rows and columns

The determinant of a square matrix is a measure of scale. For the following 2 x 2 and 3 x 3 matrices:  

    \[    A = \left[ \begin{array}{cc}a & b \\ c & d \end{array} \right]\ \ \ \ \ \ B = \left[ \begin{array}{ccc}a & b & c \\ d & e & f \\ g & h & i \end{array} \right]      \]

The determinant of matrix A, is: \ \ det(A) = ad - bc

The determinant of matrix B, is: \ \ det(B) = a(ei-fh) + b(fg-di) + c(dh-eg)

See Wikipedia for more information on determinant of a matrix.