Math 210-01: Linear Algebra: Reading Homework 4.7

1. Coordinates and Change of Basis : what do we mean by the ``coordinates of x relative to B''? what does order have to do with this? why does this make sense?
   
   1. Coordinate representation : explain what [x]_B means; how is this related to writing vectors in Rⁿ?
      
      1. finding coordinates relative to a standard basis : given the coordinate matrix for a vector x relative to a non-standard basis in Rⁿ, how can we convert to the coordinate matrix relative to the standard basis?
         
   2. Change of basis : how are the columns of a transition matrix from one basis to another related to the bases? how is it used to convert between bases?
      
      1. finding the transition matrix : how can a transition matrix between bases be found?