5. (2 points) X y + 9z = -4 -5x + 12y - 66z = 34 -3x + 10y 48z = k In order for the system of equations above to be a consistent system, k must be equal to 6. (2 points) A dietitian is planning a meal that supplies cer- tain quantities of vitamin C, calcium, and magnesium. Three foods will be used, their quantities measured in milligrams. The nutrients supplied by one unit of each food and the dietary re- quirements are given in the table below. Nutrient Food 1 Food 2 Food 3 Total Required (mg) Vitamin C 20 10 20 180 Calcium 40 40 60 480 Magnesium 40 30 60 440 Write the augmented matrix for this problem. What quantity (in units) of Food 1 is necesary to meet the di- etary requirements? What quantity (in units) of Food 2 is necesary to meet the dietary requirements? What quantity (in units) of Food 3 is necesary to meet the dietary requirements? 7. (4 points) In each part, find the matrix X solving the given equation. -6 a. X 0 1 7 4 1] . x = [ = =] 0 1 -7 b. X = 1 0 -10 3"]. x =[= =] 9 C. X = 0 1 N d. X = 4 4 2 10 -2 e. 10 0- X = 4 -10 4 0 -8 6 -10 X = O 0 f. 0 0 X = -2 O O 2X = 1 1 -1 -8 - g. 0 1 X = 6 -6 -5 0 8 -6 6 10 X = III, 1