Page 16 - 35Linear Algebra
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16 What is Linear Algebra?
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(E) What number x satisfies 4x = 1?
All of these are of the form
(?) What vector X satisfies f(X) = B?
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with a function f known, a vector B known, and a vector X unknown.
The machine needed for part (A) is as in the picture below.
x 10x
This is just like a function f from calculus that takes in a number x and
spits out the number 10x. (You might write f(x) = 10x to indicate this).
For part (B), we need something more sophisticated.
x z
y −z ,
z y − x
The inputs and outputs are both 3-vectors. The output is the cross product
of the input with... how about you complete this sentence to make sure you
understand.
The machine needed for example (C) looks like it has just one input and
two outputs; we input a polynomial and get a 2-vector as output.
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R
−1 p(y)dy
p .
R 1 yp(y)dy
−1
This example is important because it displays an important feature; the
inputs for this function are functions.
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In math terminology, each question is asking for the level set of f corresponding to B.
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