ECZ 2018 · O-Level Paper 2 · Question 1 — Matrices
Question from ECZ 2018 · O-Level Paper 2 · Question 1
(a) Given that matrix A = 4-512 and B = 8y35,
(a(i)) find the value of y for which the determinants of A and B are equal,[2]
Verified working — step 1
det A = (4)(2) - (-5)(1) = 8 + 5 = 13(a(ii)) hence find the inverse of B.[2]
Verified working — step 1
With y = 9, B = 8935 and det B = 13.(b) A small bag contains 6 black and 9 green pens of the same type. Two pens are taken at random one after the other from the bag without replacement. Calculate the probability that both pens
(b(i)) are black,[2]
Verified working — step 1
15 pens, drawn WITHOUT replacement, so 14 remain for the second draw.(b(ii)) are of different colours.[3]
Verified working — step 1
"Different colours" is black-then-green or green-then-black.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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