## zepdrix 2 years ago Linear Algebra - Linear Transformations

1. zepdrix

The table shows the amount (in g) of protein, carbohydrate, and fat supplied by one unit (100g) of three different foods.

2. zepdrix

|dw:1363858488420:dw|

3. zepdrix

Betty would like to prepare a meal using some combination of these three foods. She would like the meal to contain 15g of protein, 25g of carbohydrate, and 3g of fat. How many units of each food should she use so that the meal will contain the desired amounts of protein, carbohydrate, and fat?

4. zepdrix

I can't seem to remember how to approach this. I think it has something to do with linear transformation. hmm

5. rosho

you could probably do this on a graphing calc.

6. rosho

or you could treat each one food as x,y,and z and solve for each.

7. zepdrix

Yah I might have to resort to that. These matrices are really confusing me. Maybe I'll just rewrite it as a system of equations and figure it out that way. :p

8. rosho

much easier that way i think.

9. zepdrix

$\large 15x_1+35x_2+25x_3=15$$\large 45x_1+30x_2+50x_3=25$$\large 6x_1+4x_2+x^3=3$ Oh ok I think I'm understanding.. Maybe I'm just suppose to treat this as an augmented matrix, and then I can throw it into my calculator. $\large \left(\begin{array}{ccc|c}15&35&25&15\\45&30&50&25\\6&4&1&3\end{array}\right)$

10. zepdrix

Hmm yah it's giving me one of the multiple choices, cool. :o