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.

Type A Type B Type C
Folic acid (mg) 4 2 4
Choline (mg) 3 2 3
Inositol (mg) 3 2 4
(a) Find the inverse of the matrix below and use it to solve the remaining parts of this problem.

4 2 4

3 2 3
3 2 4

(b) How many ounces of each food should the nutritionist feed his laboratory rats if he wants their daily diet to contain 18 mg of folic acid, 15 mg of choline, and 17 mg of inositol?

Type A
oz
Type B
oz
Type C
oz

(c) How much of each food is needed to supply 10 mg of folic acid, 9 mg of choline, and 10 mg of inositol?

Type A
oz
Type B
oz
Type C
oz

(d) Will any combination of these foods supply 6 mg of folic acid, 6 mg of choline, and 7 mg of inositol?

THERE IS A COMBINATION OF FOODS GIVING THE REQUIRED SUPPLY.
THERE IS NO COMBINATION OF FOODS GIVING THE REQUIRED SUPPLY.
THIS CANNOT BE DETERMINED.

We have used the Zero-Product Property to solve algebraic equations. Matrices do not have this property. Let O represent the 2 × 2 zero matrix.

O =

0 0

0 0
FIND 2 × 2 MATRICES

A ≠ O and B ≠ O such that AB = O.

×

0 0

9 0
= O

CAN YOU FIND A MATRIX

A ≠ O such that A2 = O?

Sample Solution