MDETERM
Returns the matrix determinant of a square array. Determinants are used to solve systems of linear equations and analyze matrix invertibility.
MDETERM(array)Arguments
arrayA square numeric array (same number of rows and columns).
=MDETERM({1,2;3,4})Determinant of a 2×2 matrix
=MDETERM(A1:C3)Determinant of a 3×3 range
- •Returns #VALUE! if the array is not square or contains non-numeric values
- •A determinant of 0 means the matrix is singular (not invertible)
- •Computed with about 16 digits of precision — small rounding errors possible
- •Applying MDETERM to a non-square array, which returns a #VALUE! error since a determinant is only mathematically defined for square matrices
- •Interpreting a determinant of exactly 0 as an error rather than meaningful information - it correctly indicates the matrix is singular (not invertible), which is often the actual insight the calculation was meant to reveal
- •Assuming MDETERM's result is always a perfectly clean number - floating-point precision limits (roughly 16 digits) can introduce tiny rounding artifacts, especially for larger matrices
MINVERSECalculates a matrix's inverse, which only exists when MDETERM's result is nonzero - the two functions are closely linked in linear algebra workflows.MMULTPerforms matrix multiplication, often used alongside MDETERM and MINVERSE when solving systems of linear equations.MUNITGenerates an identity matrix, a reference point sometimes used alongside MDETERM when verifying matrix algebra results.Why does MDETERM return a #VALUE! error?
The array isn't square - it needs the same number of rows and columns for a determinant to be mathematically defined, or the array contains non-numeric values.
What does a determinant of 0 mean?
It means the matrix is singular - it has no inverse, and any system of equations it represents either has no unique solution or has infinitely many.
Why doesn't MDETERM give an exact round number I expected?
Excel computes determinants with about 16 digits of precision, which can introduce tiny floating-point rounding artifacts, especially for larger or more complex matrices - a result like 1.9999999999 instead of a clean 2 is a common symptom.
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