Editorial StaffMatrix addition is an operation performed on two matrices of the same dimensions. Let’s consider two matrices $A$ and $B$ with dimensions $m \times n$.
\[
A = \begin{bmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn} \\
\end{bmatrix}
\]
\[
B = \begin{bmatrix}
b_{11} & b_{12} & \cdots & b_{1n} \\
b_{21} & b_{22} & \cdots & b_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
b_{m1} & b_{m2} & \cdots & b_{mn} \\
\end{bmatrix}
\]
The addition of matrices $A$ and $B$, denoted by $A + B$, results in a new matrix $C$ with the same dimensions:
\[
C = A + B = \begin{bmatrix}
a_{11} + b_{11} & a_{12} + b_{12} & \cdots & a_{1n} + b_{1n} \\
a_{21} + b_{21} & a_{22} + b_{22} & \cdots & a_{2n} + b_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} + b_{m1} & a_{m2} + b_{m2} & \cdots & a_{mn} + b_{mn} \\
\end{bmatrix}
\]
In each element of the resulting matrix $C$, the corresponding elements from matrices $A$ and $B$ are added together.
Matrix addition is only defined for matrices of the same dimensions.
If the matrices have different dimensions, the addition operation is not possible.
