2 × 2 Matrix Rank
Determine rank with a floating-point tolerance tied to determinant products.
Your numbers
Numerical rank
Near-singular floating-point matrices can be numerically ambiguous. Exact symbolic rank is outside this tool.
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Formula
Rank 2 if determinant is numerically nonzero, rank 1 for a nonzero singular matrix, otherwise 0.
Determine rank with a floating-point tolerance tied to determinant products.
Worked example
- Row 1, column 1
- 1
- Row 1, column 2
- 2
- Row 2, column 1
- 3
- Row 2, column 2
- 4
- Numerical rank
- 2
- Determinant
- -2
Scope and limitations
Near-singular floating-point matrices can be numerically ambiguous. Exact symbolic rank is outside this tool.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
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Formula version: 9b827766aae3 · Example checked: