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math54-f22:quiz4

quiz-style questions:

  • Find the sign of the permutation (4312)(4312).
  • Compute det(AλI)\det(A - \lambda I) where A=[101011110]A = \begin{bmatrix} 1 & 0 & -1\cr 0 & 1 & -1\cr -1 & 1 & 0 \end{bmatrix}
  • Let σ\sigma be a permutation of length >0\ell > 0. Show that there must exist some ii such that σ(i)>σ(i+1)\sigma(i) > \sigma(i+1).
math54-f22/quiz4.txt · Last modified: 2022/09/21 10:49 by pzhou