Download your Word document
2×2 Null Space Calculator result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
2×2 Null Space Calculator — result sheet
Check a 2×2 matrix determinant and return a representative null vector when the matrix is singular.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For A=[[a,b],[c,d]], det(A)=ad−bc; when det=0, a representative null vector is (−b,a) or (−d,c).
The determinant determines whether a nonzero kernel exists, and the displayed vector is verified against the selected row direction.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Matrix a₁₁ — minimum -1000000; maximum 1000000
- Matrix a₁₂ — minimum -1000000; maximum 1000000
- Matrix a₂₁ — minimum -1000000; maximum 1000000
- Matrix a₂₂ — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Matrix a₁₁ | 1 |
| Matrix a₁₂ | 2 |
| Matrix a₂₁ | 2 |
| Matrix a₂₂ | 4 |
Determinant = 0; a representative null vector is (−2, 1).
Assumptions and limits
- The matrix is 2×2 and entries use one common numeric scale.
- A near-zero determinant is treated as singular within floating-point tolerance.
- For a nonsingular matrix the null space contains only the zero vector.
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.
No saved result was found. Please run the calculation first, then choose Download again.