To determine which matrix equation correctly shows the total number of books the Malone family has read so far this summer, we need to add the books read in June to the books read in July.
The June books are represented by the matrix:
[tex]\[
\left[
\begin{array}{ll}
7 & 1 \\
2 & 6 \\
\end{array}
\right]
\][/tex]
The July books are represented by the matrix:
[tex]\[
\left[
\begin{array}{ll}
4 & 3 \\
6 & 1 \\
\end{array}
\right]
\][/tex]
To find the total number of books read, we add the corresponding elements from each matrix:
[tex]\[
\left[
\begin{array}{ll}
7 & 1 \\
2 & 6 \\
\end{array}
\right]
+
\left[
\begin{array}{ll}
4 & 3 \\
6 & 1 \\
\end{array}
\right]
=
\left[
\begin{array}{ll}
(7 + 4) & (1 + 3) \\
(2 + 6) & (6 + 1) \\
\end{array}
\right]
\][/tex]
Performing the addition for each element:
[tex]\[
\left[
\begin{array}{ll}
11 & 4 \\
8 & 7 \\
\end{array}
\right]
\][/tex]
Therefore, the correct matrix equation is:
B. [tex]\[
\left[
\begin{array}{ll}
7 & 1 \\
2 & 6 \\
\end{array}
\right]
+
\left[
\begin{array}{ll}
4 & 3 \\
6 & 1 \\
\end{array}
\right]
=
\left[
\begin{array}{ll}
11 & 4 \\
8 & 7 \\
\end{array}
\right]
\][/tex]
