Scalar Multiplication Of Matrix Calculator

Work out scalar multiplication of matrix instantly with clear inputs, formula shown and shareable results.

About Scalar Multiplication Of Matrix Calculator

Scalar multiplication multiplies every entry by k. For an n × n matrix this scales the determinant by kⁿ, because each of the n rows is scaled independently.

Formulas

Scalar multiple

(kA)ᵢⱼ = k·Aᵢⱼ

Determinant

det(kA) = kⁿ · det(A) for an n × n matrix

Worked example

With the default values below, Scalar Multiplication Of Matrix Calculator returns k·A of [3, 6] [9, 12]. Change any input above and every figure here is recalculated in your browser.

Inputs used

Matrix, row by row: 1, 2, 3, 4
Scalar k: 3
Columns per rowaccepts 1–8: 2

Results

k·A: [3, 6] [9, 12]
Determinant multiplier kⁿ: 9.000000
det A: -2.000000
det(kA): -18.000000

Step by step

1Values used
2Scalar multiple
3Determinant
4k·A= [3, 6] [9, 12]
5Determinant multiplier kⁿ= 9.000000
6det A= -2.000000
7det(kA)= -18.000000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Multiply [[1,2],[3,4]] by 3.

[[3, 6], [9, 12]], and the determinant goes from −2 to 3² × −2 = −18.

Why kⁿ and not k?

The determinant is linear in each row separately, so scaling all n rows multiplies it n times over.