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

Matrix A = 522x. 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.

(a(i)) Given that matrix A = 522x, find the 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)) Find the inverse of A if x = 1.[2]

Verified working — step 1

With x = 1, A = 5221 and det A = 5 - 4 = …

(b(i)) A bag contains 7 red and 3 white identical balls. Two balls are taken at random one after the other without replacement. Draw a tree diagram to show all the possible outcomes.[2]

Verified working — step 1

There are 10 balls at the first draw and 9 at t…

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

Verified working — step 1

"At least one white" is the complement of "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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