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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2016 • Question 5

Question

Math 6310 • Algebra Summer 2016 • Question 5

Compute the characteristic polynomial, the minimal polynomial, and the Jordan form of the matrix \[ \begin {pmatrix} 3 & 1 & -1\\ 2 & 2 & -1\\ 2 & 2 & 0 \end {pmatrix}. \]

Raw LaTeX

Compute the characteristic polynomial, the minimal polynomial, and the Jordan form of the matrix
\[
\begin{pmatrix}
3 & 1 & -1\\
2 & 2 & -1\\
2 & 2 & 0
\end{pmatrix}.
\]

Topic Tags

Galois Groups of Polynomials Irreducible Polynomials Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization Polynomial Rings and Ring Homomorphism Kernels