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The members of the Malone family have been reading fiction and nonfiction books over the summer. So far in June and July, they have read books both in paper copies and electronically, as shown in the given tables.

\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|}{June} \\
\hline & Paper & Digital \\
\hline Fiction & 7 & 1 \\
\hline Nonfiction & 2 & 6 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|}{July} \\
\hline & Paper & Digital \\
\hline Fiction & 4 & 3 \\
\hline Nonfiction & 6 & 1 \\
\hline
\end{tabular}

Which matrix equation could the Malones use to show the total books they've read of each different type so far this summer?

A. [tex]$\left[\begin{array}{ll}6 & 2 \\ 1 & 7\end{array}\right]-\left[\begin{array}{ll}3 & 4 \\ 1 & 6\end{array}\right]=\left[\begin{array}{cc}3 & -2 \\ 0 & 1\end{array}\right]$[/tex]

B. [tex]$\left[\begin{array}{ll}7 & 1 \\ 2 & 6\end{array}\right]+\left[\begin{array}{ll}4 & 3 \\ 6 & 1\end{array}\right]=\left[\begin{array}{cc}11 & 4 \\ 8 & 7\end{array}\right]$[/tex]

C. [tex]$\left[\begin{array}{ll}6 & 2\end{array}\right]\left[\begin{array}{ll}3 & 4\end{array}\right] = \left[\begin{array}{ll}9 & 6\end{array}\right]$[/tex]



Answer :

GinnyAnswer
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]

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