This class is the 1st part of the 2 parts course, and covers Chapters 1, 2, 3 (3.1 ~3.4 only) of the textbook. To check a person's health, we don't look at only one thing, it depends on many variables, such as that person's height, weight, blood pressure, etc. We can think of these numbers as a vector in three-dimensional space. We define vector space and give a structure, set up algebraic properties which enables one to accomplish algebraic operations which applies in solving linear systems. Linear systems occur in almost alll the sciences. We develop theories and tools in solving linear systems.