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
and use it to solve the remaining parts of this problem. A calculator may be used.
1) How many ounces of each food should the nutritionist feed his laboratory rats if he wants their daily diet to contain 23 mg of folic acid, 28 mg of choline, and 27 mg of inositol?
2) How much of each food is needed to supply 20 mg of folic acid, 24 mg of choline, and 21 mg of inositol?
3) Will any combination of these foods supply 6 mg of folic acid, 8 mg of choline, and 13 mg of inositol?
A * A^-1 = Identity
The Attempt at a Solution
I have only been able to yield the inverse of the matrix:
0 1 -1
-3 5/2 0
2 -5/2 1
I do not know how to approach the rest of the problem!