ECZ 2019 · O-Level Paper 2 · Question 1 — Matrices

Question from ECZ 2019 · O-Level Paper 2 · Question 1

(a) Given that matrix A = 6x23,

(a(i)) find the value of x for which the determinant of A is 36,[2]

Verified working — step 1

det A = (6)(3) - (x)(2) = 18 - 2x

(a(ii)) hence, find the inverse of A.[2]

Verified working — step 1

With x = -9: A = 6-923 and det A = 36.

(b) A box contains 4 red pens and 5 green pens. A pen is picked at random from the box without replacement and a second pen is then picked.

(b(i)) Draw a tree diagram to illustrate the outcomes.[3]

Verified working — step 1

9 pens, drawn WITHOUT replacement, so 8 remain for the second pick.

(b(ii)) What is the probability of picking one red pen and one green pen?[2]

Verified working — step 1

"One red and one green" is red-then-green or green-then-red:

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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