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Diagonal parameter from a triangular determinant

EasyLinear Algebra~3m

The upper-triangular matrix (2510c4006)\begin{pmatrix} 2 & 5 & 1 \\ 0 & c & 4 \\ 0 & 0 & 6 \end{pmatrix} has determinant 4848. Using that, find its largest eigenvalue.

Show hints (2)+
  1. Triangular det⁡\det = product of the diagonal, so 2⋅c⋅6=48⇒c=42\cdot c\cdot 6 = 48 \Rightarrow c = 4.
  2. Triangular eigenvalues are the diagonal {2,4,6}\{2,4,6\}; the largest is 66.

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

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