Let's break down the problem step by step using the given matrix.
The matrix provided represents the driving times between four friends. The rows and columns of the matrix correspond to the friends, with the rows representing the friend who is driving and the columns representing the friend being visited.
In the provided table:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
& Fr. 1 & Fr. 2 & Fr. 3 & Fr. 4 \\
\hline
Fr. 1 & 0 & 0 & 45 & 5 \\
\hline
Fr. 2 & 8 & 0 & 23 & 11 \\
\hline
Fr. 3 & 0 & 7 & 0 & 2 \\
\hline
Fr. 4 & 35 & 21 & 0 & 0 \\
\hline
\end{tabular}
\][/tex]
To find out how many minutes Friend #1 spends driving to visit Friend #3, we need to look at the entry corresponding to the intersection of row 1 and column 3.
1. Identify the row for Friend #1: this is the first row in the matrix.
[tex]\[
[0, 0, 45, 5]
\][/tex]
2. Identify the column for Friend #3: this is the third column in the matrix.
[tex]\[
\begin{array}{c}
\text{Fr. 1} \, : \, 45, \\
\text{Fr. 2} \, : \, 23, \\
\text{Fr. 3} \, : \, 0, \\
\text{Fr. 4} \, : \, 0 \\
\end{array}
\][/tex]
3. Locate the intersection of row 1 and column 3:
The value at this intersection is 45.
Thus, the number of minutes that Friend #1 spends driving to visit Friend #3 is 45.
So the correct answer is:
[tex]\[
\boxed{45}
\][/tex]
