Linear Algebra - Linear Transformations

Question

zepdrix · Answer

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

zepdrix · Answer

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zepdrix · Answer

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?

zepdrix · Answer

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

anonymous · Answer

you could probably do this on a graphing calc.

anonymous · Answer

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

zepdrix · Answer

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

anonymous · Answer

much easier that way i think.

zepdrix · Answer

$$\large 15x_1+35x_2+25x_3=15$$$$\large 45x_1+30x_2+50x_3=25$$$$\large 6x_1+4x_2+x^3=3$$

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.

$$\large \left(\begin{array}{ccc|c}15&35&25&15\45&30&50&25\6&4&1&3\end{array}\right)$$

zepdrix · Answer

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