Chapter 6.3, Problem 61E

Nutrition 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 of these nutrients per ounce.

  

 (a) Find the inverse of the matrix $\left[\begin{array}{rrr}\hfill 3& \hfill 1& \hfill 3\\ \hfill 4& \hfill 2& \hfill 4\\ \hfill 3& \hfill 2& \hfill 4\end{array}\right]$ and use it to solve the remaining parts of this problem.  (b) How many ounces of each food should the nutritionist feed his laboratory rats if he wants their daily diet to contain 10 mg of folic acid, 14 mg of choline, and 13 mg of inositol?
 (c) How much of each food is needed to supply 9 mg of folic acid, 12 mg of choline, and 10 mg of inositol?
 (d) Will any combination of these foods supply 2 mg of folic acid, 4 mg of choline, and 11 mg of inositol?