CALCULATE WITH CONFIDENCE

Linear Algebra & Matrices

Matrix by Scalar Calculator

Multiply or divide every matrix entry by one exact scalar.

Linear Algebra & Matrices

Enter matrix values

Exact rational arithmetic
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Matrix A

Use ordinary signed decimals. Fractions, commas, and scientific notation are not accepted in this first batch.

Exact result

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Understand the subject

What does scalar multiplication do?

A scalar stretches or reverses every matrix entry by one common factor.

Use it to scale a whole linear object without changing its entry layout.

The relationship

The defining relationship

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

(cA)ᵢⱼ = c·aᵢⱼ

Interpret with care

Important boundary

Division by a scalar is undefined when the scalar is zero.

Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.

Quick guide

How to use this calculator

  1. Choose multiplication or division.
  2. Enter matrix A and the scalar.
  3. Read the exact scaled matrix.

Calculation method

Apply the scalar to each entry

Scalar multiplication multiplies every aᵢⱼ by the same value. Scalar division divides every entry and is undefined when the scalar is zero.

Worked example

Double a matrix

Multiply every entry of [[1,−2],[3,4]] by 2.

2A = [[2,−4],[6,8]]

Supported inputs

Precision and limits

Matrix size

Each input matrix may contain 1–6 rows and 1–6 columns.

Entry precision

Each signed decimal may contain up to 30 digits and 15 decimal places.

Exactness

Finite decimals are converted to reduced fractions before calculation; matrix arithmetic is not rounded.