Linear mapping/Mulled wine/Price and calories/Exercise
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On the real vector spaceof mulled wines we consider the two linear maps
We put as the price function and as the caloric function. Determine a basis for , one for and one for(Do not mind that there may exist negative numbers. In a mulled wine of course the ingredients do not come in with a negative coefficient. But if you would like to consider for example, in how many ways you can change a particular recipe, without changing the total price or the total amount of energy, then the negative entries make sense).