## Precalculus (6th Edition) Blitzer

Two matrices can be added only if they have the same numbers of rows and columns. If they are of different orders, there would be a minimum of one extra row or column in one of the matrices; there would be no element in the other matrix to be added to the elements of that extra row or column. Consider the two matrices of order $2\times 2$ $A=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)$ and $B=\left( \begin{matrix} e & f \\ g & h \\ \end{matrix} \right)$. The addition operation on the matrices is performed as follows: \begin{align} & A+B=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)+\left( \begin{matrix} e & f \\ g & h \\ \end{matrix} \right) \\ & =\left( \begin{matrix} a+e & b+f \\ c+g & d+h \\ \end{matrix} \right) \end{align} Therefore, the statement makes sense.