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3x3 Matrix Determinant — result sheet
Calculate the determinant of a bounded finite numeric 3x3 matrix in row-major order.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: det([[a,b,c],[d,e,f],[g,h,i]]) = a(ei-fh) - b(di-fg) + c(dh-eg).
Expand across the first row, compute three signed 2x2 minors, and combine them with the alternating plus-minus-plus cofactor signs. The result is one finite numeric determinant for the supplied 3x3 matrix.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Matrix entry a (row 1, column 1) — matrix units; Top-left entry of the row-major matrix.; minimum -1000000; maximum 1000000
- Matrix entry b (row 1, column 2) — matrix units; Top-middle entry of the row-major matrix.; minimum -1000000; maximum 1000000
- Matrix entry c (row 1, column 3) — matrix units; Top-right entry of the row-major matrix.; minimum -1000000; maximum 1000000
- Matrix entry d (row 2, column 1) — matrix units; Middle-left entry of the row-major matrix.; minimum -1000000; maximum 1000000
- Matrix entry e (row 2, column 2) — matrix units; Center entry of the row-major matrix.; minimum -1000000; maximum 1000000
- Matrix entry f (row 2, column 3) — matrix units; Middle-right entry of the row-major matrix.; minimum -1000000; maximum 1000000
- Matrix entry g (row 3, column 1) — matrix units; Bottom-left entry of the row-major matrix.; minimum -1000000; maximum 1000000
- Matrix entry h (row 3, column 2) — matrix units; Bottom-middle entry of the row-major matrix.; minimum -1000000; maximum 1000000
- Matrix entry i (row 3, column 3) — matrix units; Bottom-right entry of the row-major matrix.; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Matrix entry a (row 1, column 1) | 1 |
| Matrix entry b (row 1, column 2) | 2 |
| Matrix entry c (row 1, column 3) | 3 |
| Matrix entry d (row 2, column 1) | 0 |
| Matrix entry e (row 2, column 2) | 4 |
| Matrix entry f (row 2, column 3) | 5 |
| Matrix entry g (row 3, column 1) | 1 |
| Matrix entry h (row 3, column 2) | 0 |
| Matrix entry i (row 3, column 3) | 6 |
det([[1,2,3],[0,4,5],[1,0,6]]) = 1(24)-2(-5)+3(-4) = 22.
Assumptions and limits
- All nine entries are finite real numbers within the displayed bounds and are arranged row by row as [[a,b,c],[d,e,f],[g,h,i]].
- The calculation returns the determinant only; it does not infer an inverse, rank, eigenvalues, or a linear-system solution.
- Ordinary JavaScript finite-number arithmetic is sufficient for the bounded entries, but display precision is not a claim about measurement accuracy.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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