A nutritionist is studying the effects of the nutrients folic acid, choline, and inositol. He has three types of food available, and each type contains the following amounts these nutrients per ounce. Nutrients TYPE A TYPE B TYPE C Folic acid, mg CholinE, mg Inositol, mg 3 1 4 4 How much of each food is needed to supply 9 mg of folic acid, 12 mg of choline, and 10 mg of inositol? A. Set up the augmented matrix of the described linear system. Define all variables to be'used. B. Write the coefficient matrix A of the the matrix equation AX = B which is equivalent to the described linear system. C. Solve the problem either using Gauss elimination or LU decomposition.

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