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QUESTION ONE A. Consider the 2 x 2 matrices below: A - 12 91 i. Matrix multiplication is not commutative unless for very special cases. Show that for the two matrices A and B. matrix multiplication is not commutative, i.e. AB # BA ii. Show that |ABI = 141|BI 6 Marks B. Solve the following system of equations: 2x - 3y = 2 4x -6y + z =7 x + 10y = 1. 7 Marks C. A garment industry manufactures 3 shirt styles. Each style of shirt requires the services of 3 departments as listed in the table below. The cutting, sewing and packaging departments have available a maximum of 1160, 1560, and 480 labour-hours per week respectively Department Style A Style B Style C Time Cutting 0.2 0.4 0.3 1160 Sewing 0.3 0.5 0.4 1560 Packaging 0.1 0.2 0.1 480 Let x, y and z be the number of shirts to be produced for Style A, Style B and Style C respectively. Write down the system of equations involved to determine the number of each style of shirt to be produced each week for the plant to operate at full capacity in matrix form and use Cramer's rule to solve for the values of x, y and z. 12 Marks [Total Marks = 25] C