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?

Math 210-01: Linear Algebra: Reading Homework 6.3
Last Modified: Thu Apr 8 21:03:36 1999
Comments to: