MDETERM()

Syntax. MDETERM(array)

Definition. This function returns the determinant of an array.

Argument

• array (required) A numeric array with an equal number of rows and columns

Background. The calculation of the determinant is based on a numeric array. An array can be given as the following:

• A cell range (for example, A1:C3)

• An array constant (for example, {1.2.3;4.5.6;7.8.9})

• A name for a cell range or an array constant

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

Determinants are generally used for solving systems of equations. If the determinant is zero, the equation has no (definite) solution.

To calculate the determinant of array A, use the following formulas:

• If A is a 1x1 array:

  det(A) = a_1,1

• If A is a 2x2 array:

  det(A) = a₁₁ • a₂₂ – a₁₂ • a₂₁

• If A is an 3x3 array:

  det(A) = a₁₁ • a₂₂ • a₃₃ + a₁₂ • a₂₃ • a₃₁ + a₁₃ • a₂₁ • a₃₂ – a₁₃ • a₂₂ • a₃₁ – a₁₂ • a₂₁ • a₃₃ – a₁₁ • a₂₃ • a₃₂

Gottfried Leibniz (German philosopher and mathematician, 1646–1716) developed the Leibniz formula as a common formula for an n • n array:

Example. See the example for the MINVERSE() function.

See Also

MINVERSE(), MMULT(), TRANSPOSE()

Sample Files

Use the ARRAY_FUNCTION and ARRAY_FUNCTION2 worksheets in the Chapter16.xls or Chapter16.xlsx sample file. The sample files are found in the Chapter16 folder. For more information about the sample files, see the section titled Using the Sample Files.