1. Add matrices $A$ and $B$, if:

a) $A=\left(\begin{array}{rr}2 & 4 \\ -1 & 3\end{array}\right), \quad B=\left(\begin{array}{rr}-1 & 3 \\ 1 & -4\end{array}\right)$;

b) $A=\left(\begin{array}{rrr}1 & 2 & -3 \\ 2 & -4 & 5\end{array}\right), \quad B=\left(\begin{array}{rrr}2 & -4 & 1 \\ 3 & 0 & 2\end{array}\right)$;

c) $A=\left(\begin{array}{rrr}2 & 1 & 3 \\ 0 & 0 & 0 \\ -1 & 3 & 8\end{array}\right), \quad B=\left(\begin{array}{rrr}-5 & 3 & 16 \\ 0 & 0 & 0 \\ 7 & 10 & 0\end{array}\right)$,

d) $A=\left(\begin{array}{rr}2 & -1 \\ 3 & 5 \\ 0 & -8\end{array}\right), \quad B=\left(\begin{array}{rrr}1 & 0 & -3 \\ 2 & 4 & 8\end{array}\right)$.
Solution. a) Here $A$ and $B$ are square matrices of the second order. By adding their corresponding elements, we get

$$
C=A+B=\left(\begin{array}{rr}
2-1 & 4+3 \\
-1+1 & 3-4
\end{array}\right)=\left(\begin{array}{rr}
1 & 7 \\
0 & -1
\end{array}\right)
$$

b) Here $A$ and $B$ are rectangular matrices of type $2 \times 3$. We add their corresponding elements:

$$
C=A+B=\left(\begin{array}{rrr}
1+2 & 2-4 & -3+1 \\
2+3 & -4+0 & 5+2
\end{array}\right)=\left(\begin{array}{rrr}
3 & -2 & -2 \\
5 & -4 & 7
\end{array}\right)
$$

c) Here $A$ and $B$ are square matrices of the third order. We add their corresponding elements:

$$
C=A+B=\left(\begin{array}{cll}
2-5 & 1+3 & 3+16 \\
0 & 0 & 0 \\
-1+7 & 3+10 & 8+0
\end{array}\right)=\left(\begin{array}{rrr}
-3 & 4 & 19 \\
0 & 0 & 0 \\
6 & 13 & 8
\end{array}\right)
$$

d) These rectangular matrices cannot be added because $A$ is a matrix of type $3 \times 2$, and $B$ is a matrix of type $2 \times 3$; only rectangular matrices of the same type can be added.

2-4. Add matrices $A$ and $B$ :