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The condition for which the eigen values of the matrix

 

A = $\begin{pmatrix} 2 &1 \\ 1& k \end{pmatrix}$

 

are positive, is

 

a) k>1/2   b) k>-2    c) k>0   d) k< -1/2
closed as a duplicate of: Gate ME 2016: Eigen value
  • 🚩 Duplicate | 👮 Hira Thakur | 💬 “https://gateoverflow.in/234082/gate-2016-me-set-2”
asked in Linear Algebra by (131 points) 1 flag
closed by | 96 views
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for the eigen values to be positive here i think...

k+2>0 and its determinant >0

k>-2 and 2k-1>0 ---------> k>1/2

so to satisfy both the cases domain will be  k>1/2.

solution will be option A.

+1

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