brazil-enem 2012 Q169

brazil-enem · Other · enem__day2 Matrices Matrix Algebra and Product Properties
A student recorded the bimonthly grades of some of his subjects in a table. He observed that the numerical entries in the table formed a $4 \times 4$ matrix, and that he could calculate the annual averages of these subjects using matrix multiplication. All tests had the same weight, and the table he obtained is shown below.
$1^{st}$ bimonth$2^{nd}$ bimonth$3^{rd}$ bimonth$4^{th}$ bimonth
Mathematics5.96.24.55.5
Portuguese6.67.16.58.4
Geography8.66.87.89.0
History6.25.65.97.7

To obtain these averages, he multiplied the matrix obtained from the table by
(A) $\left[\frac{1}{2}\quad\frac{1}{2}\quad\frac{1}{2}\quad\frac{1}{2}\right]$
A student recorded the bimonthly grades of some of his subjects in a table. He observed that the numerical entries in the table formed a $4 \times 4$ matrix, and that he could calculate the annual averages of these subjects using matrix multiplication. All tests had the same weight, and the table he obtained is shown below.

\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
 & $1^{st}$ bimonth & $2^{nd}$ bimonth & $3^{rd}$ bimonth & $4^{th}$ bimonth \\
\hline
Mathematics & 5.9 & 6.2 & 4.5 & 5.5 \\
\hline
Portuguese & 6.6 & 7.1 & 6.5 & 8.4 \\
\hline
Geography & 8.6 & 6.8 & 7.8 & 9.0 \\
\hline
History & 6.2 & 5.6 & 5.9 & 7.7 \\
\hline
\end{tabular}
\end{center}

To obtain these averages, he multiplied the matrix obtained from the table by\\
(A) $\left[\frac{1}{2}\quad\frac{1}{2}\quad\frac{1}{2}\quad\frac{1}{2}\right]$