ECZ 2018 · O-Level Paper 2 · Question 1 — Matrices
Matrix A = 4-512 and B = 8y35. 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.
(a(i)) Given that matrix A = 4-512 and B = 8y35, 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 = …(b(i)) A small bag contains 6 black and 9 green pens of the same type. Two pens are taken at random one after the other without replacement. Calculate the probability that both pens are black.[2]
Verified working — step 1
There are 15 p…(b(ii)) Calculate the probability that the two pens are of different colours.[3]
Verified working — step 1
P(black then green) = (615)(914) = 54210The 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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