Linear Algebra I: Homework 3

Due: Friday, September 8, 2017
  1. Find the inverse of the matrix :

    We can solve for using Gaussian elimination on the augmented matrix to get :

    So,

  2. Let be the matrix with all zero entries.

    1. Is there a matrix for which ? Justify your answer.

    Yes, there are many examples. These matrices are called nilpotent matrices. For example,

    1. Is there a matrix and for which ? Justify your answer.

    Yes, there are many examples. These matrices are called idempotent matrices. For example,

  3. Find the inverse of the matrix :

    is a matrix, so we can just use the formula for the inverse.