3. A factory produces three (3) different types of paints namely Sonic, Matel and Conta. These three devices need to use three basic ingredients X, Y and Z. The requirement of the basic ingredients for the three types of paints are as mentioned below: Sonic: 10 kg of A, 10 kg of B and 5 kg of C. Matel: 7 kg of A, 5 kg of B and 4 kg of C. Conta: 4 kg of A, 2 kg of B and 3 kg of C. On one particular day the availability of the three basic components are 264kg of A, 200kg of B and 158kg of C. (a) Obtain a system of linear equations to represent above information. (3 marks) (b) Express the system of linear equations in (a) as a matrix equation. (2 marks) (c) Hence, obtain the amount (in kg) of each type of paint produced, Sonic, Matel and Conta using: (i) Cramer's method. (10 marks) (ii) Adjoint Matrix method. (10 marks) (iii) Gaussian Elimination (10 marks)