11.5 Matrices and matrix operations  (Page 2/10)

Add corresponding entries.

Add corresponding entries. Add the entry in row 1, column 1, $a_{11},$ of matrix $A$ to the entry in row 1, column 1, $b_{11},$ of $B.$ Continue the pattern until all entries have been added.

We subtract the corresponding entries of each matrix.

1. Add the corresponding entries.
   $$\begin{array}{l}\hfill \\ A+B=\left[\begin{array}{rrr}\hfill 2& \hfill -10& \hfill -2\\ \hfill 14& \hfill 12& \hfill 10\\ \hfill 4& \hfill -2& \hfill 2\end{array}\right]+\left[\begin{array}{rrr}\hfill 6& \hfill 10& \hfill -2\\ \hfill 0& \hfill -12& \hfill -4\\ \hfill -5& \hfill 2& \hfill -2\end{array}\right]\hfill \\ =\left[\begin{array}{rrr}\hfill 2+6& \hfill -10+10& \hfill -2-2\\ \hfill 14+0& \hfill 12-12& \hfill 10-4\\ \hfill 4-5& \hfill -2+2& \hfill 2-2\end{array}\right]\hfill \\ =\left[\begin{array}{rrr}\hfill 8& \hfill 0& \hfill -4\\ \hfill 14& \hfill 0& \hfill 6\\ \hfill -1& \hfill 0& \hfill 0\end{array}\right]\hfill \end{array}$$
2. Subtract the corresponding entries.
   $$\begin{array}{l}\hfill \\ A-B=\left[\begin{array}{rrr}\hfill 2& \hfill \mathrm{-10}& \hfill \mathrm{-2}\\ \hfill 14& \hfill 12& \hfill 10\\ \hfill 4& \hfill \mathrm{-2}& \hfill 2\end{array}\right]-\left[\begin{array}{rrr}\hfill 6& \hfill 10& \hfill \mathrm{-2}\\ \hfill 0& \hfill \mathrm{-12}& \hfill \mathrm{-4}\\ \hfill \mathrm{-5}& \hfill 2& \hfill \mathrm{-2}\end{array}\right]\hfill \\ =\left[\begin{array}{rrr}\hfill 2-6& \hfill \mathrm{-10}-10& \hfill \mathrm{-2}+2\\ \hfill 14-0& \hfill 12+12& \hfill 10+4\\ \hfill 4+5& \hfill \mathrm{-2}-2& \hfill 2+2\end{array}\right]\hfill \\ =\left[\begin{array}{rrr}\hfill \mathrm{-4}& \hfill \mathrm{-20}& \hfill 0\\ \hfill 14& \hfill 24& \hfill 14\\ \hfill 9& \hfill \mathrm{-4}& \hfill 4\end{array}\right]\hfill \end{array}$$