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math54-f22:quiz4

quiz-style questions:

  • Find the sign of the permutation $(4312)$.
  • Compute $\det(A - \lambda I)$ where $$A = \begin{bmatrix} 1 & 0 & -1\cr 0 & 1 & -1\cr -1 & 1 & 0 \end{bmatrix}$$
  • Let $\sigma$ be a permutation of length $\ell > 0$. Show that there must exist some $i$ such that $\sigma(i) > \sigma(i+1)$.
math54-f22/quiz4.txt · Last modified: 2022/09/21 10:49 by pzhou