M determ

MDETERM Function

The MDETERM function in Excel calculates the determinant of a square matrix provided as an array or range. Determinants are used in linear algebra to solve systems of equations, calculate inverse matrices, and more.

Syntax:

MDETERM(array)

• array: A square range of cells (e.g., A1:B2) or a 2D array constant that represents a matrix. The number of rows and columns must be equal.

Examples:

1. 2x2 Matrix
   If the range A1:B2 contains:

   2   3  
   4   5  
   

   Formula: =MDETERM(A1:B2)
   Returns: -2, because the determinant of the matrix is calculated as:
   ( (2 \times 5) - (3 \times 4) = -2 ).

2. 3x3 Matrix
   If the range A1:C3 contains:

   1   2   3  
   4   5   6  
   7   8   9  
   

   Formula: =MDETERM(A1:C3)
   Returns: 0, because the determinant of this matrix is zero.

3. Single-Cell Matrix
   Formula: =MDETERM(A1) where A1 contains 7
   Returns: 7, because the determinant of a 1x1 matrix is the value of the single element.

Usage Notes:

• The input must be a square matrix; if the number of rows and columns are not equal, Excel will return a #VALUE! error.
• Ensure all the cells in the range contain numeric values; non-numeric values will result in an error.
• The MDETERM function is particularly useful in fields like engineering, physics, and economics where matrix calculations are common.
• Determinants are often used to determine if a matrix is invertible (a matrix with a determinant of 0 is not invertible).