Math 210-01: Linear Algebra: Reading Homework 6.3

1. Matrices for Linear Transformations : why might we like matrix representations of linear transformations? how many linear transformations can we write in a matrix representation? what is the heart of doing this?
   
   1. Standard Matrices : explain how to find the standard matrix for a linear transformation
      
      1. finding standard matrices : how are the coefficients of the linear transformation (x₁,x₂,x₃)->(x₁ - 2x₂ + 5x₃, 2x₁ + 3x₃, 4x₁ + x₂ - 2x₃) related to its standard matrix?
         
   2. Composition of Linear Transformations : what is the composition of two linear transformations? how are the standard matrices of the composed linear transformations related to the standard matrix of the composition?
      
      1. general composition : how can we generalize composition? what is significant about the commutativity of composition?
         
   3. Inverse of a Linear Transformation : what does it mean to say that a linear transformation is invertible?
      
      1. invertibility : what conditions are equivalent for the invertibility of a linear transformation?