Reading notes of Linear Algebra and It's Applications (fourth editon)

Chapter 1  Linear Equations in Linear Algebra

1.1 Systems of Linear Algebra

definition ：A system of linear equation （linear system）is a collection of one or more linear equations() involvingthe  same variables. 

solutions about a system of linear equation 

Matrix Nations

the system

can be represented by matrix

called coefficient matrix

and this one

called argumented matrix

Solving a Linear System

row equipment

Existence and Uniqueness Questions？

1.2 Row Reduction And Echelon Forms 

definition：echelon form

echelon form：

reduced echelon form

THEOREM 1

Pivot Positions

defination:

Solutions of Linear System

free variable

Existence and Uniqueness Questions

THEOREM 2

what's more

1.3 Vector Equations

Vectors in  R^2

column vector (vector ,a line with arrow)

Geometric Descriptions of R^2

Vectors in R^3

Vectors in R^n

zero vector  

Linear Combinations

definations:

definations:

A Geometric Description of Span{u} and Span{u,v}

1.4 The Matrix Equation Ax=b

definition：

THEOREM 3

Existence of Solutions

THEOREM 4

Properties of Matrix-Vector Product Ax

THEOREM 5

1.5 Solutuion Set of Linear System

HomogeneousLinear System

definition：

Parametric Vector Form

Solutionss of Nohomogeneous System

THEOREM 6

1.7 Lnear Independence

defination:

THEOREM 7

THEOREM 8

THEOREM 9

1.8 Introduction to Linear Transformations

range & domain

Matrix Transformations

defination:

1.9 The Matrix of A Linear Transformation

example

THEOREM 10

Geometric Linear Transformations of R^2

Existence and Uniqueness Questions

defination:

defination:

THEOREM 11

THEOREM 12