Adding and Subtracting Matrices

Example 1:

Add the matrices.

$\left[\begin{array}{rr}\hfill 1& \hfill 5\\ \hfill -4& \hfill 3\end{array}\right]+\left[\begin{array}{rr}\hfill 2& \hfill -1\\ \hfill 4& \hfill -1\end{array}\right]$

First note that both addends are $2\times 2$ matrices, so we can add them.

$\left[\begin{array}{rr}\hfill 1& \hfill 5\\ \hfill -4& \hfill 3\end{array}\right]+\left[\begin{array}{rr}\hfill 2& \hfill -1\\ \hfill 4& \hfill -1\end{array}\right]=\left[\begin{array}{rr}\hfill 1+2& \hfill 5+\left(-1\right)\\ \hfill -4+4& \hfill 3+\left(-1\right)\end{array}\right]$

$=\left[\begin{array}{rr}\hfill 3& \hfill 4\\ \hfill 0& \hfill 2\end{array}\right]$

Example 2:

Subtract.

$\left[\begin{array}{rrr}\hfill 4& \hfill 5& \hfill 6\\ \hfill 2& \hfill 3& \hfill 4\end{array}\right]-\left[\begin{array}{rrr}\hfill 2& \hfill 4& \hfill 6\\ \hfill 1& \hfill 2& \hfill 3\end{array}\right]$

Subtract corresponding entries.

$\left[\begin{array}{rrr}\hfill 4& \hfill 5& \hfill 6\\ \hfill 2& \hfill 3& \hfill 4\end{array}\right]-\left[\begin{array}{rrr}\hfill 2& \hfill 4& \hfill 6\\ \hfill 1& \hfill 2& \hfill 3\end{array}\right]=\left[\begin{array}{rrr}\hfill 4-2& \hfill 5-4& \hfill 6-6\\ \hfill 2-1& \hfill 3-2& \hfill 4-3\end{array}\right]$

$=\left[\begin{array}{rrr}\hfill 2& \hfill 1& \hfill 0\\ \hfill 1& \hfill 1& \hfill 1\end{array}\right]$