The MDETERM function in Google Sheets is a powerful tool designed for users dealing with linear algebra and matrix computations. It calculates the determinant of a specified square matrix, which is a fundamental concept in various mathematical applications such as solving linear equations and analyzing matrix properties.

Syntax

MDETERM(matrix)

matrix - A range of cells or an array representing a square matrix.

Example #1

=MDETERM(A1:B2)

This function calculates the determinant of a 2×2 matrix defined in the cells A1 to B2. For instance, if A1=3, A2=2, B1=1, and B2=4, the result would be (34) – (21) = 10.

Example #2

=MDETERM(A1:C3)

This function determines the determinant of a 3×3 matrix located in the range A1 to C3. Supposing the values are set as A1=1, A2=0, A3=2, B1=3, B2=4, B3=5, C1=6, C2=7, C3=8, the outcome would be calculated as 1(48 – 57) – 0 + 2(37 – 46) = -6.

Example #3

=MDETERM(E1:E1)

This example attempts to compute the determinant of a 1×1 matrix in the cell E1. If E1 holds the value 5, the result is straightforwardly 5. However, if E1 is empty or contains a non-numeric entry, it will yield an error.

Error handling

• VALUE! – Indicates that the input isn’t a square matrix. Ensure the specified range has the same number of rows and columns.
• REF! – Occurs if the specified range doesn’t exist or is out of bounds. Double-check the cell references used in the function.
• NUM! – It can appear if the matrix is singular (i.e., the determinant is zero). This doesn’t prevent calculation but indicates specific properties about the matrix.

Conclusion

The MDETERM function is integral for users needing to perform matrix operations and analyze determinants in Google Sheets. Whether you’re studying linear algebra or applying these concepts to practical problems, understanding how to effectively use MDETERM allows for sophisticated data manipulation and insight generation in your spreadsheets.