Math 210-01: Linear Algebra: Reading Homework 1.3--2.1

1. Applications of Systems of Linear Equations :
   
   1. Polynomial Curve Fitting : what are we doing in the course of polynomial curve fitting? how do systems of linear equations arise in this context? what are the variables in the equations?
      
      1. translation : how does the book obtain a ``nicer'' polynomial when faced with large x-values?
         
      2. application : what galactic application does the book fit a polynomial for? what important lesson do we learn from this example?
         
   2. Network Analysis : what is a network in this context?
      
2. Matrices and Operations with Matrices : who was Arther Cayley? what careers did he pursue?
   
   1. Notation and Equality : how do we denote matrices? what is true about the elements of equal matrices?
      
   2. Operations : how are matrices added? how are the entries of a matrix changed by scalar multiplication?
      
   3. Multiplication : how are the rows and columns of matrices combined in matrix multiplication?
      
      1. commutivity : is the product of matrices, A B, the same as B A?
         
      2. linear systems : how is a linear system of equations written as a matrix equation?
         
      3. linear combinations : what is a linear combination of column matrices?