## Precalculus (6th Edition) Blitzer

Consider the matrices having $A$ and $B$ of different order: $A=\left[ \begin{matrix} 1 & 0 \\ 2 & 3 \\ \end{matrix} \right]=\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}} \\ {{a}_{21}} & {{a}_{22}} \\ \end{matrix} \right]$ And $B=\left[ \begin{matrix} 1 & 0 & 0 \\ 2 & 3 & 1 \\ 0 & 0 & 1 \\ \end{matrix} \right]=\left[ \begin{matrix} {{b}_{11}} & {{b}_{12}} & {{b}_{13}} \\ {{b}_{21}} & {{b}_{22}} & {{b}_{23}} \\ {{b}_{31}} & {{b}_{32}} & {{b}_{33}} \\ \end{matrix} \right]$ Then, ${{a}_{11}}$ is added with ${{b}_{11}}$, ${{a}_{12}}$ is added with ${{b}_{12}}$, but there is no corresponding element in A that can be added with ${{b}_{13}}$. Therefore, two matrices of different order cannot be added.