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Linear Transformations
A function is a rule that assigns a value from a set B for each element in a set A.
Notation: f : A B
If the value b B is assigned to value a A, then write f (a) = b, b is called the image of a under f .
A is called the domain o
1
Introduction
Math 120 Basic Linear Algebra I
This is a math class, expect abstract thinking and deductive reasoning a lot!
You will learn to prove theorems, and to apply their results in solving problems.
Some examples, but focus on the theory
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Elementary Matrices and a Method for Finding the Inverse
Denition 1
A n n matrix is called an elementary matrix if it can be obtained from In by performing a single
elementary row operation
Reminder: Elementary row operations:
1. Multiply a row a by k
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1.1
Euclidean Vector Spaces
Euclidean n-space
In this chapter we will generalize the ndings from last chapters for a space with n dimensions, called n-space. Denition 1 If n N\cfw_0, then an ordered n-tuple is a sequence of n numbers in R: (a1 , a2 , .
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Systems Of Linear Equations and Matrices
1.1
Systems Of Linear Equations
In this section youll learn what Systems Of Linear Equations are and how to solve them.
Remember that equations of the form
a1 x + a2 y = b, for a1 , a2 R\cfw_0, b R
describe lines