ECZ 2025 · O-Level Paper 2 · Question 1 — Matrices
Question from ECZ 2025 · O-Level Paper 2 · Question 1
(a) Given that matrix L = -2-267 and matrix M = x-4-32, find the
(a(i)) value of x, for which the determinant of matrices L and M are equal,[2]
Verified working — step 1
The determinant of abcd is ad - bc.(a(ii)) inverse of matrix L.[2]
Verified working — step 1
For a 2 × 2 matrix the inverse swaps the main-diagonal entries, changes the sign of the other two, and divides by the determinant.(b) A boy uses two different buses to go to school. On a particular day, the probability that the first bus is late is 0.2 and the probability that the second bus is not late is 0.7. Find the probability that on this day
(b(i)) both buses are late,[2]
Verified working — step 1
P(second bus not late) = 0.7 is given, so P(second late) = 1 - 0.7 = 0.3.(b(ii)) only one bus is late.[3]
Verified working — step 1
"Only one late" happens two ways: first late with second on time, or first on time with second late.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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