ECZ 2020 · O-Level Paper 2 · Question 1 — Matrices

Question from ECZ 2020 · O-Level Paper 2 · Question 1

(a) Given that matrix A = 522x, find the

(a(i)) value of x for which A has no inverse,[2]

Verified working — step 1

A matrix has no inverse when its determinant is zero.

(a(ii)) inverse of A if x = 1.[2]

Verified working — step 1

With x = 1: A = 5221 and det A = 5 - 4 = 1.

(b) A bag contains 7 red and 3 white identical balls. Two balls are taken from the bag at random one after the other without replacement.

(b(i)) Draw a tree diagram to show all the possible outcomes.[2]

Verified working — step 1

10 balls, drawn WITHOUT replacement, so 9 remain for the second draw.

(b(ii)) Find the probability of taking at least one white ball.[3]

Verified working — step 1

"At least one white" is easiest via its complement, "both 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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