To represent Aliane's flight information in a matrix, we need to organize the flight times between the cities in a systematic way. A flight matrix shows the flight times from each departing city to each arriving city.
Here, we will construct a 4x4 matrix for the cities A, B, C, and D, with rows representing the departing cities and columns representing the arriving cities.
### Step-by-Step Solution:
1. Determine the size of the matrix:
Since there are 4 cities (A, B, C, D), we will create a 4x4 matrix.
2. Initialize the matrix:
- Each entry [tex]\([i][j]\)[/tex] in the matrix will represent the flight time from city [tex]\(i\)[/tex] to city [tex]\(j\)[/tex].
- If there is no direct flight between the cities, we set the value to 0.
3. Update the matrix based on given flight times:
- From City A:
- To City B: 4.2 hours
- To City C: 3.9 hours
- From City B:
- To City A: 5.1 hours
- To City D: 9.5 hours
- From City C:
- To City B: 1.7 hours
- To City D: 2.2 hours
- From City D:
- To City A: 10.5 hours
- To City B: 8.6 hours
### Constructing the Flight Time Matrix:
Let's fill the matrix step by step:
```
Flight Matrix (Departing from rows, arriving at columns):
A B C D
A [[ 0, 4.2, 3.9, 0 ],
B [ 5.1, 0, 0, 9.5 ],
C [ 0, 1.7, 0, 2.2 ],
D [10.5, 8.6, 0, 0 ]]
```
So, the final flight time matrix is:
[tex]\[ \begin{matrix}
& A & B & C & D \\
A & 0 & 4.2 & 3.9 & 0 \\
B & 5.1 & 0 & 0 & 9.5 \\
C & 0 & 1.7 & 0 & 2.2 \\
D & 10.5 & 8.6 & 0 & 0
\end{matrix} \][/tex]
Thus, the matrix that correctly represents Aliane's flight information is:
[tex]\[ \begin{bmatrix}
0 & 4.2 & 3.9 & 0 \\
5.1 & 0 & 0 & 9.5 \\
0 & 1.7 & 0 & 2.2 \\
10.5 & 8.6 & 0 & 0
\end{bmatrix} \][/tex]
