Solve the Problem $N _ { 1 }$ Represents the Number of City and Highway Miles Driven for Gal/mi)

question 2

Multiple Choice

Solve the problem.
-Matrix G represents the gas mileage (in gal/mi) for city and highway driving for four models of car. Matrix $N _ { 1 }$ represents the number of city and highway miles driven for one trip. Matrix $N _ { 3 }$ represents The number of city and highway miles driven for three trips. $\quad$$\text { City}$$\quad$ $\text {Highway }$
$G=\left[\begin{array}{cc} \frac{1}{23} & \frac{1}{30} \\\\\frac{1}{24} & \frac{1}{37} \\\\\frac{1}{24} & \frac{1}{30} \\\\\frac{1}{25} & \frac{1}{31}\end{array}\right] \text { Car } 1 \text { automatic } 1 \text { manual }$
$N _ { 1 } = \left[ \begin{array} { l } 110 \\ 260 \end{array} \right] \begin{array} { l } \text { Number of city miles } \\ \text { Number of highway miles } \end{array}$


a. Find the product $G N _ { 1 }$ and interpret its meaning. Round each entry to 1 decimal place.
b. Find the product $G N _ { 3 }$ and interpret its meaning. Round each entry to 1 decimal place. This matrix represents the number of gallons of gasoline used for each model of car for each of the three
Trips.

• A) a. \( G N_{1}=\left[\begin{array}{l}13.4 \\ 11.6 \\ 13.3 \\ 12.8\end{array}\right] \) This matrix represents the number of gallons of gasoline used for each model of car for 110 mi driven In the city and 260 mi driven on the highway. \[\text { b. } G N _ { 3 } = \left[ \begin{array} { l l l } 12.3 & 16.9 & 13.4 \\ 10.3 & 14.5 & 11.6 \\ 12.2 & 16.7 & 13.3 \\ 11.8 & 16.1 & 12.8 \end{array} \right] \text {. }\]
• B) a. \(G N_{1}=\left[\begin{array}{l} 15.0 \\ 13.8 \\ 14.5 \\ 13.9 \end{array}\right]\) This matrix represents the number of gallons of gasoline used for each model of car for 260 mi driven In the city and 110 mi driven on the highway. b. \(G N _ { 3 } = \left[ \begin{array} { c c c } 13.4 & 16.9 & 12.3 \\ 11.6 & 14.5 & 10.3 \\ 13.3 & 16.7 & 12.2 \\ 12.8 & 16.1 & 11.8 \end{array} \right]\) This matrix represents the number of gallons of gasoline used for each model of car for each of the three Trips.
• C) a. \(G N_{1}=\left[\begin{array}{l} 13.4 \\ 11.6 \\ 13.3 \\ 12.8 \end{array}\right]\) This matrix represents the number of gallons of gasoline used for each model of car for 110 mi driven In the city and 260 mi driven on the highway. \[\text { b. } G N _ { 3 } = \left[ \begin{array} { l l l } 16.9 & 13.4 & 12.3 \\ 14.5 & 11.6 & 10.3 \\ 16.7 & 13.3 & 12.2 \\ 16.1 & 12.8 & 11.8 \end{array} \right]\] This matrix represents the number of gallons of gasoline used for each model of car for each of the three Trips.
• D) a. \(G N _ { 1 } = \left[ \begin{array} { l } 13.4 \\ 11.6 \\ 13.3 \\ 12.8 \end{array} \right]\) This matrix represents the number of gallons of gasoline used for each model of car for 110 mi driven In the city and 260 mi driven on the highway. \[\text { b. } G N _ { 3 } = \left[ \begin{array} { l l l } 13.4 & 16.9 & 12.3 \\ 11.6 & 14.5 & 10.3 \\ 13.3 & 16.7 & 12.2 \\ 12.8 & 16.1 & 11.8 \end{array} \right] \text {. }\] This matrix represents the number of gallons of gasoline used for each model of car for each of the three Trips.

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