Example

• There are some rabbits and chicken in the barn. What will be their respective numbers if there are 94 legs and 35 heads in total?
  
  

• Suppose that there are number of chickens and number of rabbits, then we get
  
  

Exercise

• solve the following linear systems:

• 
  
  

• 
  
  

• 
  
  

Leads of this course

• A linear system may
  (1) admits a unique solution
  (2) has infinitely many solutions
  (3) admits no solution
  How do we judge and (if possible) solve it systematically
  
  

• Linear maps: modern perspectives and notations
  
  

Contents of this course

（1）Vectors and linear dependences

（2）Representing linear maps：matrices and their arithmetics

（3）Solutions to linear systems (structures and approaches)

（4）Eigenpairs and diagonalization

Dependencies

• (1)-->(2)+(3)-->(4)
  
  

• 1-3 lectures for each part
  
  

• 1 exercise session for each part

Brief history

• Solving and systems：thousand years ago
  Ancient Babylon | Nine Chapters on the Mathematical Art
  
  

• Determinants：17th-18th century，by Leibniz, Cramer, Euler
  
  

• Early forms and concepts of matrices: 19th century
  by Gauss, Sylvester, Cayley
  
  

• Extensive use and developments: after middle 20th century