Page 367 - 35Linear Algebra

G

Movie Scripts

G.1 What is Linear Algebra?

Hint for Review Problem 5
Looking at the problem statement we find some important information, first
that oranges always have twice as much sugar as apples, and second that the
information about the barrel is recorded as (s, f), where s = units of sugar in
the barrel and f = number of pieces of fruit in the barrel.
We are asked to find a linear transformation relating this new representation
to the one in the lecture, where in the lecture x = the number of apples and
y = the number of oranges. This means we must create a system of equations
relating the variable x and y to the variables s and f in matrix form. Your
answer should be the matrix that transforms one set of variables into the
other.
Hint: Let λ represent the amount of sugar in each apple.
1. To find the first equation relate f to the variables x and y.
2. To find the second equation, use the hint to figure out how much sugar
is in x apples, and y oranges in terms of λ. Then write an equation for s
using x, y and λ.

G.2 Systems of Linear Equations

Augmented Matrix Notation

Why is the augmented matrix

1 1 27
,
2 −1 0
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