In a special diet for a hospital​ patient, the total amount per meal of food groups​ A, B, and C must equal 330 g. The diet should include​ one-third as much of group A as of group​ B, and the sum of the amounts of group A and group C should equal twice the amount of group B. How many grams of each food group should be​included? (Give answers to the nearest​ tenth.) Solve the problem using matrices.

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