. For matrices 2 5 A=E 3 '61] B: 1 o C: 3 1 Find (a) 2A+BT (b) AB (e) C"1 . Solve by the method of matrix row-reduction: x+yz =7 2m3y2z =4 xy5z =23 . Solve by the method of matrix row-reduction: 233y+z =0 m+2yz =0 z+y+z =0 . Solve AX = B if 8 65 5 4 3 10 7 6 (2 marks) (2 marks) (4 marks) (4 marks) (4 marks) (2 marks) \"[35 :11 -=:[ :1]: hr and H.21- . Solve using the inverse of the coefcient matrix: 5$+4y3z =2 10x7y+62 =5 8x6y+5z =1 (HINT: take a look at matrix C in question 1c) (4 marks) 6. Sketch a graph to solve the following system of inequalities. Clearly label the intercepts of the boundary lines and the corners of the feasible region. {4 marks) 2I+3y 0 y > 0 7. Maximize Z = 5m + 3y subject to: (9 marks) 3+ 2y 5 10 x S 4 y 2 1 may 2 0 Clearly state the maximum value of Z subject to these constraints and the coordinates (1:,y) at which it occurs. 8. A produce grower is purchasing fertilizer containing three nutrients: A, B, and C. The minimum weekly requirements are 80 units of A, 120 units of B, and 240 units of C. There are two blends of fertilizer on the market: Blend I costs $8 per bag, and contains 2 units of A, 6 units of B, and 4 units of C. Blend 11 costs $10 per bag, and contains 2 units of A, 2 units of B, and 12 units of C. How many bags of each blend should the grower buy each week in order to minimize the cost while still meeting the nutrient requirements? (12 marks)