Math 210-01: Linear Algebra: Reading Homework 6.2

1. The Kernel and Range of a Linear Transformation : what question is considered in this section?
   
   1. the Kernel : what is the kernel of a linear transformation? how can we find the kernel of a linear transformation?
      
      1. properties of the kernel : what can we say about the kernel of a linear transformation? what alternate terminology is therefore sometimes used for the kernel? why?
         
   2. the Range : what is the range of a linear transformation? what is special about it?
      
      1. properties of the range : what is true about the range of a linear transformation defined to be the product of a vector with a given matrix?
         
      2. rank and nullity : how are the rank and nullity of a linear transformation defined? how are these related to the dimension of the domain of the transformation?
         
   3. One-to-One and Onto Transformations : what are one-to-one and onto linear transformations?
      
   4. Isomorphisms : what is an ismorphism? what are ismorphic vector spaces?
      
      1. isomorphic vector spaces : under what circumstances will finite-dimensional vector spaces by isomorphic? how does the book prove this in the ``assume that the vector spaces have dimension n'' direction?