Page 9 - 35Linear Algebra

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What is Linear Algebra?

Many difficult problems can be handled easily once relevant information is
organized in a certain way. This text aims to teach you how to organize in-
formation in cases where certain mathematical structures are present. Linear
algebra is, in general, the study of those structures. Namely

Linear algebra is the study of vectors and linear functions.

In broad terms, vectors are things you can add and linear functions are
functions of vectors that respect vector addition. The goal of this text is to
teach you to organize information about vector spaces in a way that makes
problems involving linear functions of many variables easy. (Or at least
tractable.)
To get a feel for the general idea of organizing information, of vectors,
and of linear functions this chapter has brief sections on each. We start
here in hopes of putting students in the right mindset for the odyssey that
follows; the latter chapters cover the same material at a slower pace. Please
be prepared to change the way you think about some familiar mathematical
objects and keep a pencil and piece of paper handy!

1.1 Organizing Information

Functions of several variables are often presented in one line such as
f(x, y) = 3x + 5y .

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