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Two-by-Two Adjoint Matrix Calculator — result sheet
Calculate the adjoint matrix and determinant of a supplied two-by-two matrix.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For [[a,b],[c,d]], adj(A)=[[d,−b],[−c,a]] and det(A)=ad−bc.
The adjoint is the cofactor-transpose matrix for the two-by-two case, shown with its determinant so the inverse condition is visible.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Entry a — minimum -1000000; maximum 1000000
- Entry b — minimum -1000000; maximum 1000000
- Entry c — minimum -1000000; maximum 1000000
- Entry d — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Entry a | 1 |
| Entry b | 2 |
| Entry c | 3 |
| Entry d | 4 |
Adjoint =[[4,-2],[-3,1]]; determinant =-2.
Assumptions and limits
- All entries use one numeric scale.
- The adjoint exists for every finite matrix, while an inverse would additionally require a nonzero determinant.
- No rounding or symbolic expression is inferred beyond the supplied decimal values.
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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