Determine Whether the Linear Transformation T Is One-To-One and Whether $15 \mathrm {~g}$

Multiple Choice

Determine whether the linear transformation T is one-to-one and whether it maps as specified.
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Betty would like to prepare a meal using some combination of these three foods. She would like the meal to contain $15 \mathrm {~g}$ of protein, $25 \mathrm {~g}$ of carbohydrate, and $3 \mathrm {~g}$ 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? Round to 3 decimal places.

A) $0.326$ units of Food 1, $0.247$ units of Food 2, $0.059$ units of Food 3
B) $0.280$ units of Food 1, $0.192$ units of Food 2, $0.164$ units of Food 3
C) $0.360$ units of Food 1, $0.204$ units of Food 2, $0.055$ units of Food 3
D) $0.302$ units of Food 1, $0.238$ units of Food 2, $0.085$ units of Food 3