Math 210-01: Linear Algebra: Reading Homework 1.1--1.2

1. What is Linear Algebra? : what is the ``most fundamental'' theme of linear algebra? what is one of our early goals for the course?
   
   1. Theoretical Linear Algebra : what is the central theoretical topic of linear algebra?
      
   2. Definition : what definition is given for linear algebra?
      
2. Systems of Linear Equations : who was Gauss? what did he do?
   
   1. Introduction : what is a linear equation in $n$ variables? a nonlinear equation? a solution to a linear equation? a solution set?
      
   2. Systems : what is a system of linear equations? what does the double subscript notation $a_{ij}$ in the book's example indicate?
      
      1. solutions : when is a system of linear equations consistent? inconsistent?
         
      2. number of solutions : how many solutions may there be to a linear system of equations?
         
      3. solving a system : how does back substitution from row-echelon form work? what are equivalent systems? how may an equivalent system be produced from a given system?
         
3. Gaussian Elimination and Gauss-Jordan Elimination :
   
   1. Matrices : what is a matrix? what is the augmented matrix for a system of linear equations? the coefficient matrix?
      
      1. row operations : define elementary row operations; what is suggested when doing them?
         
      2. solving linear systems : how are elementary row operations used to solve a linear system?
         
   2. Row-Echelon Form : what is row-echelon form of a matrix? reduced row-echelon form?
      
   3. Gaussian Elimination : what is Gaussian elimination with back-substitution?
      
      1. Gauss-Jordan Elimination : how is Gauss-Jordan elimination different from Gaussian elimination? which is better?
         
   4. Homogeneous Systems : what is a homogeneous linear system? what solution is ``obvious''?
      
      1. solutions of homogeneous systems : what solutions are there to a homogeneous system?