Adding matrices combines tables of data – sales of several products over several months, or two transformations’ displacement fields. It works entry by entry.
How to use the Matrix Addition and Subtraction 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
Corresponding entries are added or subtracted. The matrices must have the same number of rows and columns.
Formula
(A ± B)ᵢⱼ = aᵢⱼ ± bᵢⱼ
Worked example
Inputs — Operation: Addition A + B; Matrix size (rows × columns): 2 × 2; a₁: 4; b₁: 1; a₂: 1; b₂: 3; B: x₁: 1; B: y₁: 2; B: x₂: 0; B: y₂: 1.
Results — Result = ⎡ 5 3 ⎤
⎣ 1 4 ⎦.
Key terms
- Element-wise
- Operating on matching entries.
Frequently asked questions
Can I add a 2 × 3 matrix and a 3 × 2 matrix?
No – the sizes must match.
Is matrix addition commutative?
Yes, A + B = B + A.
What is the zero matrix?
The matrix of all zeros, the identity for addition.
How do I subtract?
Subtract each entry of B from the matching entry of A.