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2×2 LU Decomposition Calculator — result sheet
Decompose a 2×2 matrix into lower-unit and upper-triangular factors and verify their determinant.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For A=[[a,b],[c,d]], L=[[1,0],[c/a,1]] and U=[[a,b],[0,d−bc/a]], when a≠0.
The factors are multiplied back conceptually through the displayed entries, while the pivot boundary is rejected rather than silently dividing by zero.
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 | 4 |
| Matrix a₁₂ | 3 |
| Matrix a₂₁ | 6 |
| Matrix a₂₂ | 8 |
L₂₁ = 1.5; U₁₁ = 4; U₁₂ = 3; U₂₂ = 3.5; determinant = 14.
Assumptions and limits
- This page uses a 2×2 Doolittle factorization without row pivoting.
- The leading pivot a must be nonzero.
- The factors are numerical and do not replace stability analysis for larger or ill-conditioned systems.
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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