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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

- Homework: 2, 4, 9, 10 and the following problems:
- 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