CAPE Pure Mathematics Unit 2 · May/June 2023 · Paper 2 · Question 5(a)(i)
A matrix is given as M = [[1, 1, -1], [1, 2, -k], [1, -k, -1]].
Calculate the determinant of M.
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Practise this questionOther parts of this question
- 5(a)(ii)Hence, or otherwise, determine the values of k for which the simultaneous equations x + y - z = 1, x + 2y - kz = 0, x - ky - z = 1 have a unique solution.[4 marks]
- 5(a)(iii)Using k = 2 in the matrix, M, solve the system of linear equations by first reducing it to row echelon form.[6 marks]
- 5(b)(i)Draw a tree diagram to represent the possible events and their respective probabilities.[4 marks]
- 5(b)(ii)Determine the probability that at least one pencil taken from the bag is blue.[4 marks]
- 5(b)(iii)Determine whether the result of the second draw is independent of the first draw. Justify your response.[2 marks]
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