In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2.

Let matrix A represent the matrix with the following elements: .
Let matrix B represent the matrix with the following elements: .
The player i is the top-ranked player if the sum of row i in the matrix A + B is the largest. What is the number of this player?

Question

​In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​​

Let matrix A represent the matrix with the following elements:  .
Let matrix B represent the matrix with the following elements:  .
The player i is the top-ranked player if the sum of row i in the matrix A + B is the largest. What is the number of this player?
​

Quizplus · Accepted Answer

To find the sum of each row in the matrix A+B, we add the corresponding entries in A and B.

Row 1: (0+1), (2+0), (1+1), (1+0), (0+1) = 2,2,2
Row 2: (1+0), (0+2), (0+0), (0+2), (1+0) = 1,2,0
Row 3: (0+1), (0+0), (2+0), (1+1), (1+0) = 1,0,2
Row 4: (2+0), (2+0), (1+0), (0+1), (0+0) = 2,2,1
Row 5: (1+0), (1+1), (1+1), (2+0), (0+0) = 1,2,2

From this, we can see that the sum of row 2 is the smallest (1+2+0=3), making player 2 the least likely top-ranked player. The sum of row 3 is the largest (1+0+2=3), making player 3 the most likely top-ranked player. Therefore, the answer is A) player 3.

​In Order to Rank the Five Members of Its Chess

In Order to Rank the Five Members of Its Chess