MDETERM function

The MDETERM function in Excel calculates the determinant of a square matrix.

Syntax

=MDETERM(array)

Parameters

• array: A range of cells containing the square matrix for which you want to calculate the determinant. The matrix must have the same number of rows and columns (i.e., it must be a square matrix).

Return Value

The function returns the determinant of the matrix, which is a scalar value.

How It Works

The determinant of a matrix is a special number that can be calculated from its elements. For a 2×2 matrix:

$$\text{Determinant} = (a \times d) – (b \times c)$$

For larger matrices (3×3 or beyond), the determinant is calculated using a more complex method, but the concept remains the same.

Example Usage

Example 1: 2×2 Matrix

Suppose you have the following 2×2 matrix:

You can calculate the determinant using:

=MDETERM(A1:B2)

Result: -2

Explanation: The determinant of this 2×2 matrix is calculated as $(1 \times 4) – (2 \times 3) = 4 – 6 = -2$.

Example 2: 3×3 Matrix

If you have a 3×3 matrix in the range A1:C3:

You can calculate the determinant using:

=MDETERM(A1:C3)

Result: 0

Explanation: The determinant of this matrix is 0 because the rows (or columns) are linearly dependent (the third row is a sum of the first two rows).

Example 3: Using a Larger Matrix

For a larger matrix, simply select the range corresponding to the square matrix (e.g., a 4×4 matrix in the range A1:D4) and apply the MDETERM function.

Important Notes

• Square Matrix Requirement: The matrix must be square (same number of rows and columns). If it isn’t, Excel will return a #VALUE! error.
• Matrix Determinant: The determinant of a matrix is used in various mathematical and scientific calculations, such as solving systems of linear equations and finding matrix inverses.

This function is helpful when working with linear algebra problems and matrix operations.