Definition: Let \(A=[a_{ij}]\) and \(B=[b_{ij}]\) be two matrices with the same size, say \(m \times n\). The sum of \(A\) and \(B\), written \(A+B\), is the matrix obtained by adding corresponding elements from A and B. ié:
\(A + B =\)
\[\begin{bmatrix}
a_{11}+b_{11} & a_{12}+b_{12} & \dots & a_{1n}+b_{1n}\\
a_{21}+b_{21} & a_{22}+b_{22} & \dots & a_{2n}+b_{2n}\\
\vdots & \vdots & \ddots & \vdots\\
a_{m1}+b_{m1} & a_{m2}+b_{m2} & \dots & a_{mn}+b_{mn}
\end{bmatrix}\]
Few theorems that may facilitate calculations of matrix addition:
a) \((A + B) + C = A + (B + C)\);
b) \(A + 0 = 0 + A = A\);
c) \(A + (-A) = (-A) + A = 0\);
d) \(A + B = B + A\).
