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6 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2023 · Paper 2 · Question 5(a)(iii)

A matrix is given as M = [[1, 1, -1], [1, 2, -k], [1, -k, -1]].

Using k = 2 in the matrix, M, solve the system of linear equations by first reducing it to row echelon form.

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Other parts of this question

  1. 5(a)(i)Calculate the determinant of M.[5 marks]
  2. 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]
  3. 5(b)(i)Draw a tree diagram to represent the possible events and their respective probabilities.[4 marks]
  4. 5(b)(ii)Determine the probability that at least one pencil taken from the bag is blue.[4 marks]
  5. 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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