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Vectors and matrices — Question 6

QCAA 2024, Paper 1 · 1 mark

Q6 · 2024 · Technology-freeSimple familiar1 mark

QUESTION 6

Players P, Q, R and S played each other once in a competition where there were no draws.
Only the following results are known. • Player P defeated players Q and R. • Player Q defeated two players. • Players R and S each defeated one player.
Based on these results, a dominance matrix NN was partially constructed as shown.
PQRS
P0110
Q
R0001
S1000
The completed matrix NN is
(A)
[0110100100011000]\begin{bmatrix}0&1&1&0\\1&0&0&1\\0&0&0&1\\1&0&0&0\end{bmatrix}
(B)
[0110001100011000]\begin{bmatrix}0&1&1&0\\0&0&1&1\\0&0&0&1\\1&0&0&0\end{bmatrix}
(C)
[0110000100011000]\begin{bmatrix}0&1&1&0\\0&0&0&1\\0&0&0&1\\1&0&0&0\end{bmatrix}
(D)
[0110010100011000]\begin{bmatrix}0&1&1&0\\0&1&0&1\\0&0&0&1\\1&0&0&0\end{bmatrix}
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