Linear Algebra & Matrices

Matrix Addition Calculator

Add two equally sized matrices entry by entry with exact arithmetic.

Linear Algebra & Matrices

Enter matrix values

Exact rational arithmetic
Matrix A
Matrix B

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

Exact result

Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

  1. Give A and B matching dimensions.
  2. Enter every matrix value.
  3. Read and copy the exact sum.

Calculation method

Add corresponding entries

If A and B have the same number of rows and columns, the entry in row i and column j of A + B is aᵢⱼ + bᵢⱼ.

Worked example

Add two 2 × 2 matrices

Add each entry of [[1,2],[3,4]] to the entry in the same position of [[5,6],[7,8]].

[[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]]

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.