CAPE Pure Mathematics Unit 2 · May/June 2022 · Paper 2 · Question 5(a)(i)
A matrix P is given as P = [[4, 3, 5], [9, 4, 15], [12, 10, -3]].
Show that |P| = 183.
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- 5(a)(ii)Hence, or otherwise, show that the adjoint of P is adj(P) = [[-162, 59, 25], [207, -72, -15], [42, -4, -11]].[5 marks]
- 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]
- 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]
- 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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