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Matrix: Additional questions set 2 1. A zoo veterinarian can purchase animal food of three different types: A, B and C. Each food comes in the same size bag and the number of grams of each of three nutrients (N1,N2, N3) in each bag is summarised in the following table A B C N1 5 5 10 N2 10 5 30 N3 15 15 10 For one animal, the veterinarian determines that she needs to combine the food types to get 10,000g of N1, 20,000 of N2 and 20,000g of N3 (a) Write down the matrix equation (Ax b) representing the problem. (b Use Gauss Jordan method to obtain the inverse of the matrix A in part (a (c) Use the answer from (b) to determine how many bags of each type of food should she order? (d) If she would like to change the number of grams for each nutrients to be 8000g of N1, 18,400 of N2 and 19,000 of N3, determine how many bags of each type. of food that she need for her new order 1080 0.8 0.2 0.2 1000 d) 20 Ans., b) o 0.7 0.2 0.15 0 0.05 500 250 2 4 -8 0 0 1 -9 a 1 a a 2. Given A 0 0 0 3 1 a az 2 0 0 (a If det(-18A) det (B D detC, find the determinant of D b Find the adjoint of Cadi C and use it to show that C 1 1 1 (c) Find the complete solution to C x 2 1 -4 41 Ans a) -108(1-a2), b) 2 2 2 c) 1 0 2
Show transcribed image text Matrix: Additional questions set 2 1. A zoo veterinarian can purchase animal food of three different types: A, B and C. Each food comes in the same size bag and the number of grams of each of three nutrients (N1,N2, N3) in each bag is summarised in the following table A B C N1 5 5 10 N2 10 5 30 N3 15 15 10 For one animal, the veterinarian determines that she needs to combine the food types to get 10,000g of N1, 20,000 of N2 and 20,000g of N3 (a) Write down the matrix equation (Ax b) representing the problem. (b Use Gauss Jordan method to obtain the inverse of the matrix A in part (a (c) Use the answer from (b) to determine how many bags of each type of food should she order? (d) If she would like to change the number of grams for each nutrients to be 8000g of N1, 18,400 of N2 and 19,000 of N3, determine how many bags of each type. of food that she need for her new order 1080 0.8 0.2 0.2 1000 d) 20 Ans., b) o 0.7 0.2 0.15 0 0.05 500 250 2 4 -8 0 0 1 -9 a 1 a a 2. Given A 0 0 0 3 1 a az 2 0 0 (a If det(-18A) det (B D detC, find the determinant of D b Find the adjoint of Cadi C and use it to show that C 1 1 1 (c) Find the complete solution to C x 2 1 -4 41 Ans a) -108(1-a2), b) 2 2 2 c) 1 0 2