Math 210-01: Linear Algebra: Reading Homework 2.4

1. Elementary Matrices : what do we see in this section?
   
   1. Elementary Matrices (Def) : what is the definition of an elementary matrix? give two examples of 2x2 elementary matrices
      
      1. elementary matrices and row operations : how are elementary matrices related to elementary row operations? give a 3x3 elementary matrix to swap the first and third rows of a 3xn matrix.
         
      2. row reduction and elementary matrices : how can we row reduce using elementary matrices? is the order of operations significant? (is the order in which the row operations in row reduction significant? explain)
         
   2. Elementary Matrices and Invertibility : how are elementary matrices and matrix invertibility related? why are there two parts to the theorem on this subject?
      
   3. Systems and Matrices : what five statements are introduced as equivalent by the book?
      
   4. LU-Factorization : what is LU-factorization? why is it useful?
      
      1. finding LU-factorizations : when does a matrix have an LU-factorization? how can it be found?
         
      2. LU-factorization and linear systems : how can the LU-factorization of a matrix be used to solve a linear system?