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Matrix Addition — result sheet
Add two finite row-major 3x3 matrices entry by entry and return their deterministic matrix sum.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Cij = aij + bij for each row i and column j from 1 through 3.
Matrix addition pairs entries that occupy the same row and column in two equal-sized matrices. The result keeps the fixed row-major 3x3 layout and contains no reordering, multiplication, or hidden scalar conversion.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- A11 — matrix entry; Row 1, column 1 of matrix A.; minimum -1000; maximum 1000
- A12 — matrix entry; Row 1, column 2 of matrix A.; minimum -1000; maximum 1000
- A13 — matrix entry; Row 1, column 3 of matrix A.; minimum -1000; maximum 1000
- A21 — matrix entry; Row 2, column 1 of matrix A.; minimum -1000; maximum 1000
- A22 — matrix entry; Row 2, column 2 of matrix A.; minimum -1000; maximum 1000
- A23 — matrix entry; Row 2, column 3 of matrix A.; minimum -1000; maximum 1000
- A31 — matrix entry; Row 3, column 1 of matrix A.; minimum -1000; maximum 1000
- A32 — matrix entry; Row 3, column 2 of matrix A.; minimum -1000; maximum 1000
- A33 — matrix entry; Row 3, column 3 of matrix A.; minimum -1000; maximum 1000
- B11 — matrix entry; Row 1, column 1 of matrix B.; minimum -1000; maximum 1000
- B12 — matrix entry; Row 1, column 2 of matrix B.; minimum -1000; maximum 1000
- B13 — matrix entry; Row 1, column 3 of matrix B.; minimum -1000; maximum 1000
- B21 — matrix entry; Row 2, column 1 of matrix B.; minimum -1000; maximum 1000
- B22 — matrix entry; Row 2, column 2 of matrix B.; minimum -1000; maximum 1000
- B23 — matrix entry; Row 2, column 3 of matrix B.; minimum -1000; maximum 1000
- B31 — matrix entry; Row 3, column 1 of matrix B.; minimum -1000; maximum 1000
- B32 — matrix entry; Row 3, column 2 of matrix B.; minimum -1000; maximum 1000
- B33 — matrix entry; Row 3, column 3 of matrix B.; minimum -1000; maximum 1000
Worked example
| Input | Value |
|---|---|
| A11 | 1 |
| A12 | 2 |
| A13 | 3 |
| A21 | 0 |
| A22 | 1 |
| A23 | 4 |
| A31 | 5 |
| A32 | 6 |
| A33 | 0 |
| B11 | 2 |
| B12 | 0 |
| B13 | 1 |
| B21 | 1 |
| B22 | 3 |
| B23 | 0 |
| B31 | 0 |
| B32 | 2 |
| B33 | 1 |
A + B = [[3, 2, 4], [1, 4, 4], [5, 8, 1]].
Assumptions and limits
- A and B are real square 3x3 matrices written in the fixed row-major key order a11 through a33 and b11 through b33.
- Every entry is a finite number in the inclusive range -1000 through 1000, and the arithmetic result must remain finite.
- The matrices share a compatible mathematical context; no units, basis change, rounding policy, or symbolic expression is inferred.
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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