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The condition for which the eigenvalues of the matrix  $A=\begin{bmatrix} 2 & 1\\ 1 &k \end{bmatrix}$   are positive is

  1. $k > \frac{1}{2}$
  2. $ k > −2$
  3. $ k > 0$
  4. $k< \frac{-1}{2}$
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By the properties of eigen values, if all the principal minors of A are possitive then all the eigen values of A are also possitive.

so  |A2*2| > 0

ie 2k - 1 > 0

k>1/2

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