Page 05 MARKS 7. Matrices P and Q are defined by 2 5 1 x P ⎛ ⎞ = ⎜ ⎟ − − ⎝ ⎠ and 2 3 4 Q y − ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ , where ,x y ∈\. (a) Given the determinant of P is 2, obtain: (i) The value of x. (ii) 1 P−. (iii) 1 P−Q′, where Q′ is the transpose of Q. (b) The matrix R is defined by , 5 2 where 6 R z z − ⎛ ⎞ = ∈ ⎜ ⎟ − ⎝ ⎠ \. Determine the value of z such that R is singular. 8. Use the Euclidean algorithm to find integers a and b such that 1595a + 1218b = 29. 9. Solve ( ) 2 2 1 x dy e y dx = + given that when x = 0, y = 1. Express y in terms of x. 10. n S is defined by 2 1 1 3 n r r r = ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ ∑ . (a) Find an expression for n S , fully factorising your answer. (b) Hence find an expression for 2 2 10 1 3 p r r r = ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ ∑ where p > 5. [Turn over 1 1 2 2 4 5 2 2