Matrix Addition Calculator
Add two matrices element-wise with dimension validation and step-by-step output.
Inputs
A + B
6 8 10 12
Dimensions
2×2
Step by step
Matrix A
= 1 2 3 4
Matrix B
= 5 6 7 8
A + B (element-wise)
= 6 8 10 12
How it works
Matrix addition adds corresponding elements of two matrices of the same dimensions. If A and B are both m×n matrices, then (A+B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ.
Formula
Matrix Addition
(A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ
- A
- First matrix
- B
- Second matrix
Frequently Asked Questions
Can I add matrices of different sizes?
No. Matrix addition requires both matrices to have the same dimensions (same number of rows and columns).
Is matrix addition commutative?
Yes. A + B = B + A for all conforming matrices, since addition of real numbers is commutative.
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