Page 416 - 35Linear Algebra

416 Movie Scripts

as a demonstration of changing basis.
Since this was a linear systems problem, we can try to represent what’s in
the barrel using a vector space. The first representation was the one where
(x, y) = (apples, oranges):

Oranges

(x, y)

Apples

Calling the basis vectors ~e 1 := (1, 0) and ~e 2 := (0, 1), this representation would
label what’s in the barrel by a vector

x
~x := x~e 1 + y~e 2 = ~e 1 ~e 2 .
y
Since this is the method ordinary people would use, we will call this the
‘‘engineer’s’’ method!
But this is not the approach nutritionists would use. They would note the
amount of sugar and total number of fruit (s, f):

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