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2D Vector Independence Calculator — result sheet
Determine whether two two-dimensional vectors are linearly independent from their determinant.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For v₁=(x₁,y₁), v₂=(x₂,y₂), determinant=x₁y₂−x₂y₁; nonzero determinant means independent.
In two dimensions, the determinant is the signed parallelogram area and provides a compact independence test.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vector 1 x — minimum -1000000; maximum 1000000
- Vector 1 y — minimum -1000000; maximum 1000000
- Vector 2 x — minimum -1000000; maximum 1000000
- Vector 2 y — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Vector 1 x | 1 |
| Vector 1 y | 2 |
| Vector 2 x | 2 |
| Vector 2 y | 3 |
Determinant = −1; the vectors are linearly independent.
Assumptions and limits
- Both vectors are expressed in the same two-dimensional basis.
- Floating-point values within a small tolerance are treated as zero determinant.
- The result concerns the two supplied vectors only, not a larger set.
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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