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5 marksMatrices and Systems of Linear Equations

CAPE Pure Mathematics Unit 2 · May/June 2022 · Paper 2 · Question 5(a)(ii)

A matrix P is given as P = [[4, 3, 5], [9, 4, 15], [12, 10, -3]].

Hence, or otherwise, show that the adjoint of P is adj(P) = [[-162, 59, 25], [207, -72, -15], [42, -4, -11]].

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Other parts of this question

  1. 5(a)(i)Show that |P| = 183.[4 marks]
  2. 5(a)(iii)Solve the system of linear equations [[4, 3, 5], [9, 4, 15], [12, 10, -3]] [[x], [y], [z]] = [[11], [13], [4]].[8 marks]
  3. 5(b)Alex has five blue marbles, four green marbles and three red marbles. In how many ways can he arrange four marbles in a row, if the marbles of any given colour…[4 marks]
  4. 5(c)Let A and B be two events such that P(A) = 1/2, P(B) = 1/4 and P(A ∩ B) = 1/8. Calculate the value of P(A' ∩ B').[4 marks]

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