Scalar multiplication scales a matrix – converting units in a table of data, scaling a transformation or forming linear combinations of matrices.
How to use the Matrix by Scalar Calculator
- Choose the matrix size – the matching grid of fields appears.
- Enter the entries row by row (a₁ b₁ c₁ is the first row, a₂ b₂ c₂ the second, and so on).
- Read the result; integer matrices give exact fractions.
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Each entry is multiplied by k. Multiplying by −1 gives the negative of the matrix; by 0 the zero matrix.
Formula
(k·A)ᵢⱼ = k · aᵢⱼ
Worked example
Inputs — Matrix size (rows × columns): 2 × 3; a₁: 4; b₁: 1; c₁: 2; a₂: 1; b₂: 3; c₂: 0; Scalar k: 1.5.
Results — Result of k · A = ⎡ 6 1.5 3 ⎤
⎣ 1.5 4.5 0 ⎦.
Key terms
- Scalar
- A single number.
Frequently asked questions
What is scalar multiplication?
Multiplying every entry by the same number.
Does it change the determinant?
det(kA) = kⁿ det(A) for an n × n matrix.
Is k·A the same as A·k?
Yes.
What happens with k = 0?
You get the zero matrix.