Scalar Matrix Multiplication Calculator
Multiply every matrix entry by scalar k
2x2 Matrix
3x3 Matrix
Multiply by Scalar
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Scalar Matrix Multiplication Formula
Scalar multiplication scales every entry of a matrix by the same number. It keeps the matrix shape unchanged while changing each value proportionally.
⚠ Scalar multiplication works for any matrix size. This page provides 2x2 and 3x3 inputs consistent with the matrix tools category.
How Scalar Matrix Multiplication Works
Scalar matrix multiplication is the simplest matrix scaling operation. Each entry is multiplied independently by the same scalar value.
Same Scalar
Every entry uses the same multiplier k.
Same Dimensions
The result keeps the original matrix size.
Distributive
k(A+B)=kA+kB when sizes match.
Scaling Effect
Positive, negative, or zero scalars change values predictably.
Example: For k = 3 and A = [[1,2],[3,4]], kA = [[3,6],[9,12]].
Applications of Scalar Matrix Multiplication
Matrix Scaling
Vector Spaces
Linear Algebra
Numerical Methods
Physics Models
Frequently Asked Questions
What is scalar matrix multiplication?▼
It multiplies every entry of a matrix by the same scalar number k.
What is the scalar multiplication formula?▼
For C = kA, each entry is cij = k times aij.
How do I use this kA calculator?▼
Enter Matrix A, enter scalar k, and calculate. The tool multiplies every entry by k.
Does scalar multiplication change matrix size?▼
No. The result has the same dimensions as the original matrix.
Where is scalar multiplication used?▼
It is used in vector spaces, scaling transformations, numerical methods, physics models, and matrix algebra.
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