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Determinant from trace and one eigenvalue

EasyLinear Algebra~3m

A 2×22\times 2 matrix AA has tr A=7\mathrm{tr}\,A = 7, and one of its eigenvalues is 22. What is det⁡A\det A?

Show hints (2)+
  1. Trace = sum of eigenvalues, so the other eigenvalue is 7−2=57 - 2 = 5.
  2. det⁡=\det = product of eigenvalues =2⋅5= 2 \cdot 5.

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Asked at: Probability & Market-Making, Data-Driven Research

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