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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

APPLICATIONS

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.

Type A Type B Type C
Folic acid (mg) 3 1 3
Choline (mg) 4 2 4
Inositol (mg) 3 2 4

(a) Find the inverse of the matrix

[ 3 1 3 4 2 4 3 2 4 ]

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 2mg of folic acid, 4 mg of choline, and 11 mg of inositol?

To determine

(a)

To find:

The inverse of the matrix [313424324].

Explanation

Approach:

Take a 3×6 matrix with left half as matrix B and right half as I3 and transform the left half into identity matrix by performing elementary row operations on the entire matrix, the right half becomes inverse of the matrix B.

Calculation:

Consider A=[313424324]

Take a matrix of dimension 3×6 with left half as matrix B and right half as I3 and perform row operations to transform the left half into I3.

[313100424010324001]R113R1[11311300424010324001]R2R24R1[1131130002304310324001]R3R33R1[1131130002304310011101]R2R3[1131130001110102304310]

R1R113R2[1023230130111

To determine

(b)

To find:

The ounces of each food the nutritionist should feed his laboratory rats in order to keep their daily diet to contain 10 mg of folic acid, 14 mg of choline, and 13 mg of inositol.

To determine

(c)

To find:

The ounces of each food the needed to supply 9 mg of folic acid, 12 mg of choline, and 10 mg of inositol.

To determine

(d)

To find:

The combination of food that can supply 2 mg of folic acid, 4 mg of choline, and 11 mg of inositol.

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