## 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