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".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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question