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4 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 2 · Question 5(b)(ii)

A and B are two matrices given as A = [[2, x, -1], [3, 0, 2], [2, 1, 0]] and B = [[1, 2, 5], [2, 3, 4], [2, 1, 2]].

Given that det(AB) = -10, show that x = 2.

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Other parts of this question

  1. 5(a)(i)How many numbers made up of five digits can be made from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number contains exactly one even digit and no digit is…[4 marks]
  2. 5(a)(ii)Determine the probability that the number formed in (a)(i) is less than 30 000.[4 marks]
  3. 5(b)(i)Determine the value of x for which A⁻¹ does NOT exist.[4 marks]
  4. 5(b)(iii)Hence, obtain A⁻¹.[4 marks]
  5. 5(c)(i)Given that 40% of the individuals selected green and 50% selected blue, calculate the probability that an individual selected BOTH colours.[3 marks]
  6. 5(c)(ii)Determine the total number of individuals who participated in the experiment.[2 marks]

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