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Matrix by Scalar — result sheet
Multiply every entry of one finite row-major 3x3 matrix by one bounded scalar.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: B = sA, so bij = scalar x aij for every row i and column j from 1 through 3.
Scalar multiplication scales every matrix entry by the same number. The operation preserves the 3x3 shape and the row-major positions while allowing positive, zero, negative, and fractional scale factors within the bounded contract.
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
- Scalar — scalar; The finite number applied to every entry of A.; 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 |
| Scalar | 2 |
2A = [[2, 4, 6], [0, 2, 8], [10, 12, 0]].
Assumptions and limits
- A is a real 3x3 matrix in the fixed row-major a11 through a33 order.
- The scalar and all matrix entries are finite numbers in the inclusive range -1000 through 1000, and every product must remain finite.
- The scalar is an algebraic scale factor; no unit conversion, normalization, or matrix-matrix multiplication 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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