Question: 3 a For the networks given in Question 1, interpret the information given by the sum of the second column of each matrix.
b For the networks given in Question 2, explain what the sum of the first column of each matrix represents.
1. **Stating the problem:**
We need to interpret the sums of specific columns in the matrices representing networks of towns A, B, and C.
2. **Recall the meaning of the matrices:**
Each matrix entry $m_{ij}$ represents the number of direct ways from town $i$ (row) to town $j$ (column).
3. **Part a: Sum of the second column in Question 1 matrices**
- The second column corresponds to town B.
- Summing the second column means adding all $m_{iB}$ for $i = A, B, C$.
- This sum represents the total number of direct ways from all towns to town B.
4. **Part b: Sum of the first column in Question 2 matrices**
- The first column corresponds to town A.
- Summing the first column means adding all $m_{iA}$ for $i = A, B, C$.
- This sum represents the total number of direct ways from all towns to town A.
5. **Summary:**
- The sum of a column in these matrices gives the total number of direct connections leading into the town represented by that column.
**Final answers:**
- (a) The sum of the second column in Question 1 matrices tells us how many direct routes lead into town B from all towns.
- (b) The sum of the first column in Question 2 matrices tells us how many direct routes lead into town A from all towns.