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Linear Algebra - Linear Transformations

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

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I can't seem to remember how to approach this. I think it has something to do with linear transformation. hmm
you could probably do this on a graphing calc.
or you could treat each one food as x,y,and z and solve for each.
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
much easier that way i think.
\[\large 15x_1+35x_2+25x_3=15\]\[\large 45x_1+30x_2+50x_3=25\]\[\large 6x_1+4x_2+x^3=3\] 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. \[\large \left(\begin{array}{ccc|c}15&35&25&15\\45&30&50&25\\6&4&1&3\end{array}\right)\]
Hmm yah it's giving me one of the multiple choices, cool. :o

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