14 4. (i) A is a 2 by 2 matrix and B is a 2 by 3 matrix. Giving a reason for your answer, explain whether it is possible to evaluate (a) AB (b) A + B (2) (ii) Given that −         − − −         5 3 1 0 0 0 5 0 2 12 1 1 11 3 a b a b = λI where a, b and λ are constants, (a) determine • the value of λ • the value of a • the value of b (b) Hence deduce the inverse of the matrix −         5 3 1 0 0 a b a b (3) (iii) Given that M = 1 1 1 0 sin cos 0 cos2 sin 2 θ θ θ θ         where 0  θ < π determine the values of θ for which the matrix M is singular. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________