Section 2.1 Matrix addition and scalar multiplication
Subsection 2.1.1 Matrix addition
Let \(A\) and \(B\) be two matrices of the same size, say \(m \times n\text{.}\) The sum of \(A\) and \(B\text{,}\) denoted by \(A + B\text{,}\) is the matrix obtained by adding corresponding entries of \(A\) and \(B\text{.}\) That is, if \(A = [a_{ij}]\) and \(B = [b_{ij}]\text{,}\) then:
\begin{equation*}
A + B = [a_{ij} + b_{ij}]
\end{equation*}
Subsection 2.1.2 matrix-scalar-multiplication
For any scalar (real number) \(c\text{,}\) the scalar multiple of \(A\) by \(c\text{,}\) denoted by \(cA\text{,}\) is the matrix obtained by multiplying each entry of \(A\) by \(c\text{.}\) That is:
\begin{equation*}
cA = [ca_{ij}]
\end{equation*}
