Page 20 - 35Linear Algebra
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20 What is Linear Algebra?
linear transformation L means that L(u) can be thought of as multiplying
the vector u by the linear operator L. For example, the linearity of L implies
that if u, v are vectors and c, d are numbers, then
L(cu + dv) = cLu + dLv ,
which feels a lot like the regular rules of algebra for numbers. Notice though,
that “uL” makes no sense here.
Remark A sum of multiples of vectors cu + dv is called a linear combination of
u and v.
1.4 So, What is a Matrix?
Matrices are linear functions of a certain kind. They appear almost ubiqui-
tously in linear algebra because– and this is the central lesson of introductory
linear algebra courses–
Matrices are the result of organizing information related to linear
functions.
This idea will take some time to develop, but we provided an elementary
example in Section 1.1. A good starting place to learn about matrices is by
studying systems of linear equations.
Example 5 A room contains x bags and y boxes of fruit.
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