Addition and Subtraction of Matrices

As long as you can add and subtract the ``things'' in your matrices, you can add and subtract the matrices themselves. The addition and subtraction occurs in the obvious way--element by element. Here are a couple of examples:

$\displaystyle \begin{pmatrix}1 & 3 & 7 \\ 2 & 6 & -4 \\ 2 & 15 & \pi \end{pmatr...
...n{pmatrix}
4 & 5 & 8 \\ 7.5 & 9 & -4-e \\ 4 & 20 & \pi + \sqrt{2} \end{pmatrix}$

$\displaystyle \begin{pmatrix}1 & 3 & 7 \\ 2 & 6 & -4 \\ 2 & 15 & \pi \end{pmatr...
...{pmatrix}
-2 & 1 & 6 \\ -3.5 & 3 & e-4 \\ 0 & 10 & \pi - \sqrt{2} \end{pmatrix}$

To find what goes in row $ i$ and column $ j$ of the sum or difference, just add or subtract the entries in row $ i$ and column $ j$ of the matrices being added or subtracted.

In order to make sense, both of the matrices in the sum or difference must have the same number of rows and columns. It makes no sense, for example, to add a $ 2\times 4$ matrix to a $ 3\times 4$ matrix.