Spring 2019

Math 5120 Graduate Algebra II

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Homework 3

Due Monday April 15, in class.

  • Section 12.2
    • Homework: 2, 4, 9, 10 and the following problems:
      • 26. Find all similarity types (in rational canonical form) of rational \(3 \times 3\) matrices \(A\) that satisfy the equation \(A(A - 2I)^2 = 0\). (Source: Derek J.S. Robinson, "Abstract Algebra (Second Edition)", De Gruyter, Berlin/Boston (2015))
      • 27. Find the invariant factors and rational canonical form of the rational matrix \[ \left[ \begin{array}{ccc}2&3&1\\ 1&2&1\\ 0&0&-4 \end{array}\right].\] (Source: Derek J.S. Robinson, "Abstract Algebra (Second Edition)", De Gruyter, Berlin/Boston (2015))
    • Hand In: 26, 27
  • Section 12.3
    • Homework: 1, 5, 8, 11
    • Hand In: 11
  • Section 10.4
    • Homework: 2, 3, 4, 6, 7, 8, 11, 12, 15, 16, 19, 27
    • Hand In: 2, 11, 27