A dietitian is planning a meal that supplies certain quantities of vitamin C, calcium, and magnesium. Three foods containing these nutrients will be used. The amount of each nutrient, in milligrams, found in one unit of each food is given in the table below, along with the dietary requirements. --m --m --m (a) Write the augmented matrix for this problem: 30 60 30 300 50 120 60 570 20 60 40 300 (b) What quantity of Food 1 is necessary to meet the dietary requirements? Answer: units (0) What quantity of Food 2 is necessary to meet the dietary requirements? Answer: units (d) What quantity of Food 3 is necessary to meet the dietary requirements? Answer: | units The reduced row echelon form of a system of linear equations in 9: and y or in 9:, y and z is given. For each system, determine whether it has a unique solution, infinitely many solutions, or no solutions. (a) 1 0 0 2 0 1 0 2 0 0 0 0 GA. No solutions 0 B. Infinitely many solutions QC. Unique solution: 3 = 2, y = 2 O D. Unique solutionm: : 2, y : 2 OE. Unique solution: a": = 0,3; = 0, z = 0 O E None of the above (b) 1 0 0 2 0 1 0 1 0 0 0 2 QA. Unique solution: a: : 2,y : 1 O B. No solutions QC. Unique solution: 3 = 2, y = 1, z = 2 OD. Unique solution: a: : 2,y : 1,z : 0 O E. Infinitely many solutions O F. None of the above (C) QA. Unique solution: a: = 0, y = 0 Q B. No solutions QC. Unique solution: :1: : 0, y : 0, z : 0 O D. Unique solution: :1: : 1,3; : 1, z = O Q E. Infinitely many solutions O F. None of the above ((11) Q A. Infinitely many solutions Q B. No solutions QC. Unique solution: :13 : 0, y : 3 O D. Unique solution: :1: : 0, y : 3, z : 2 Q E. Unique solution: cc : 3,3; : 2 O F. None of the above OCH 1 00 0 10 0 00 OHO HOD DOD