To determine which of the given options represents a vector from one of the rockets, we need to consider the data provided in the [tex]\(5 \times 3\)[/tex] matrix:
[tex]\[
\left[\begin{array}{lll}
4 & 8 & 9 \\
5 & 1 & 7 \\
9 & 6 & 3 \\
2 & 4 & 8 \\
3 & 2 & 1
\end{array}\right]
\][/tex]
From this matrix, each row constitutes a vector representing the trajectory data of a rocket. Specifically, the vectors represented by each row are:
1. [tex]\([4, 8, 9]\)[/tex]
2. [tex]\([5, 1, 7]\)[/tex]
3. [tex]\([9, 6, 3]\)[/tex]
4. [tex]\([2, 4, 8]\)[/tex]
5. [tex]\([3, 2, 1]\)[/tex]
Next, we need to examine each given option to see if any matches one of these vectors:
1. [tex]\[
\left[\begin{array}{lll}
4 & 8 & 9 \\
5 & 1 & 7 \\
9 & 6 & 3
\end{array}\right]
\][/tex]
This option is structured as a [tex]\(3 \times 3\)[/tex] matrix, not a single vector from the original [tex]\(5 \times 3\)[/tex] matrix.
2. [tex]\((9+6+3)=18\)[/tex]
This option is a calculation resulting in the scalar value 18, which does not represent a vector.
3. [tex]\[
\left[\begin{array}{ll}
4 & 8 \\
5 & 1 \\
9 & 6 \\
2 & 4 \\
3 & 2
\end{array}\right]
\][/tex]
This option is structured as a [tex]\(5 \times 2\)[/tex] matrix, not a single vector from the original [tex]\(5 \times 3\)[/tex] matrix.
4. [tex]\[
\left[\begin{array}{l}
9 \\
7 \\
3 \\
8 \\
1
\end{array}\right]
\][/tex]
This option is structured as a [tex]\(5 \times 1\)[/tex] column matrix, not a single vector from the original [tex]\(5 \times 3\)[/tex] matrix.
By examining the options, none of them match the vectors directly taken from the rows of the original [tex]\(5 \times 3\)[/tex] matrix. Therefore, none of the given options are correct representations of a single vector from the original set of trajectories.
