1. If A =

,`

.| p pp 342and det A = 14, find the possible values of p.Working:Answers:..............(Total 4 marks)2. Let M =

,`

.|122a, where a .(a) Find M2 in terms of a.(4)(b) If M2 is equal to

,`

.| 5445, find the value of a.(2)Using this value of a, find Ml and hence solve the system of equations:x + 2y = 32x y = 3(6)(Total 12 marks) 13. A and B are 2 2 matrices, where A =]]]

0225 and BA = ]]]

824411.Find B.Working:Answers:..............(Total 4 marks)4. The matrices A, B, X are given byA = ,6 5 1 3

,`

.| B = ,3 08 4

,`

.| X = ,

,`

.|d cb a where a, b, c, d .Given that AX + X = , find the exact values of a, b, c and d.(Total 8 marks)5. Consider the matrix A =

,`

.|1 72 5.(a) Write down the inverse, Al.(2)(b) B, C and X are also 2 2 matrices.(i) Given that XA + B = C, express X in terms of A1, B and C.(ii) Given that B =

,`

.|2 57 6, andC = ,7 8 0 5

,`

.| find X.(4)(Total 6 marks) 26. Let A =

,`

.|0 cb a and B =

,`

.|e d0 1. Giving your answers in terms of a, b, c, d and e,(a) write down A + B;(b) find AB.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(Total 6 marks) 37. (a) Write down the inverse of the matrix A =

,`

.|3 5 11 2 21 3 1(b) Hence solve the simultaneous equationsx 3y + z = 12x + 2y z = 2x 5y + 3z = 3............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(Total 6 marks)8. Let C =

,`

.|7412 and D =

,`

.| a215.The 2 2 matrix Q is such that 3Q = 2C D(a) Find Q.(3)(b) Find CD.(4)(c) Find D1.(2)(Total 9 marks) 4 5