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e) A manufacturer produces three products: Product A, Product B and Product C. To be able to produce each product he uses a combination of three distinct inputs namely Input I, Input II and Input III the supply of which is currently at 730,350 and 350 units respectively. Each unit of Product A requires 6 units of Input I, 3 units of Input II and 4 units of Input III to be produced. Similarly, each unit of Product B requires 8 units of Input 1 and 4 units of Input II while Product C uses 5 units of Input I, 1 unit of Input II and 3 units of Input III. (i) Let a, b and c represent the number of units produced of Products A,B and C respectively. The manufacturer must decide what quantity of each product to produce so that his entire supply of inputs is utilized. Formulate his/her decision in the form of a system of three linear equations in the variables a,b and c. [3 marks] (ii) Rewrite the above system of linear equations in the matrix form Ax=b. [2 marks ] (iii) Hence or otherwise, determine how many units of product B that can be manufactured. [5 marks] 3) a) Given; A=3740112,B=[691014121525] and C=711617940 Use the above matrices to find the following: (i) BC [1 marks] (ii) ACT [4 marks] (iii) 2C10A [3 marks] b) Two matrices H and M are said to be similar/identical. Given that H=x+2b24m539c and M=m724dcdv+x914 (i) Calculate the values for m and x. [3 marks] c) Given that A=634840513 (i) Calculate values for the cofactors C31,C32 and C33. [3 marks] (ii) Hence or otherwise, determine A. [2 marks] d) Use the below system of equations to answer the following: 12x3y=574x+10y=30 From the matrix form for the system of equations above, find A1. [4 marks]

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