How do you calculate the inverse of a matrix? Can you at least do that?
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?
Well you got that far so thats good. Now you are being told to use that inverse. Why? Do you remember how to do matrix multiplication? Your 3X3 matrix (the original) is the coefficients for three systems of equations, with three unknowns correct:
The last matrix represents the total amount of each food type.
In your Part A, you are being asked, how much Folic, Choline and Inositol to use use, if you know the amount of F, C, I you will end up. In English: "How much of each type of Folic should I use to get 23mg's of Folid. . .etc" If you represented the matrix equation as a regular equation wouldn't you have:
A*v=Total, where v are the individual amounts of the A, B, and C varieties of the food-stuffs. So wouldn't v = Total/A? But this is just Total*1/A, and 1/A is just A^-1 - the inverse matrix. Do you see where this is going? Let me know if you are still stuck (you really shouldn't be though).