PlanMaker MDETERM: Determinants, Row Operations and Singular Matrices

The PlanMaker 2026 reference, 2024 reference and 2021 reference document this function. Original introduction and last-working-version endpoints remain unverified; a manual family is not a test of every build or edition.

References were retrieved on October 15, 2026. No native PlanMaker execution was performed. Examples below are independently calculated expectations, not application screenshots or native results. FreeOffice/mobile edition coverage and file transfers are not certified. English formulas use commas; verify separators and names in your installation.

=MDETERM(Array)

Array is a numeric cell range or array constant. It must be square, with the same number of rows and columns, and contain only numbers. The result is a single determinant, not a matrix of element-by-element determinants.

A determinant of zero means the matrix is singular mathematically. A nonzero determinant establishes invertibility in exact arithmetic; its size alone does not certify that a floating-point inversion is well conditioned. This guide does not assign undocumented native errors to non-square ranges, text or blank cells.

Create DeterminantControls and enter these numbers in A2:B3:

Enter =MDETERM(A2:B3) in F2. The independent expected result is 10, from 4×6−7×2. For a visible check, F3 =A2*B3-B2*A3 also gives 10. A 2×2 determinant is not the sum of the four entries, nor the product of only the diagonal entries.

In a copy change A2 from 4 to 5. Both expected results become 16. The lower row and the second column are unchanged, so the six-unit increase comes from the changed first entry multiplied by its cofactor 6.

Enter the following separate matrix in J2:L4:

=MDETERM(J2:L4) has expected result −40, matching the official constant-array example =MDETERM({9,8,8;2,4,6;1,2,1}). Expanding along the first row gives 9×(4−12)−8×(2−6)+8×(4−4)=−40.

The array notation reference uses semicolons between rows. Column separators depend on locale; the example’s commas follow the US-style notation. A range with visible cells avoids confusing array separators with ordinary function-argument separators.

Starting from the original 2×2 matrix, swapping its rows gives −10. Multiplying only its first row by 3 gives matrix rows 12,21 and 2,6, whose determinant is 30. Adding twice the first row to the second gives rows 4,7 and 10,20, still with determinant 10.

Use separate copies for each control rather than applying all operations cumulatively. The changed signs and factors describe different transformations. Multiplying every element of this 2×2 matrix by 3 gives determinant 90, because two rows were each scaled by 3; it does not merely triple the original determinant.

The matrix with rows 1,2 and 2,4 has determinant 0 because the second row is twice the first. The corresponding linear equations are not independent. MINVERSE explicitly documents #NUM! for a singular matrix; that is a statement about MINVERSE, not an extra MDETERM error rule.

For the upper-triangular matrix with rows 2,7,1; 0,3,8; 0,0,5, the determinant is 30, the product of diagonal entries 2×3×5. This convenient shortcut applies to triangular matrices; it would give the wrong answer for the original general 2×2 matrix.

The matrix with rows 1,1 and 1,1.001 has exact decimal determinant 0.001. It is mathematically invertible, but its rows are close to dependent. An application uses finite precision, so a robust workflow should examine residuals and sensitivity instead of treating a nonzero displayed determinant as a universal accuracy guarantee.

If a displayed value rounds to zero, increase the displayed precision and inspect the underlying value. Conversely, a tiny computed nonzero number does not prove that an intended exact singular relation was entered accurately.

Check that the selected input excludes headers and contains a complete square. A 2×3 block is not made square by selecting a 3×3 output area. MDETERM returns one scalar, so the multi-cell entry steps for MINVERSE/MMULT are unnecessary for the examples here.

No native maximum matrix size, overflow threshold, coercion or complete error matrix was established. Keep source matrices visible, record the exact build, and validate small known determinants before relying on a larger numeric model.