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Differential Equations

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Moderate

Two Distinct, Real, Positive Eigenvalues of Matrix

DIFFEQ-EGH5LU

Find all values of the constant $a$ for which the matrix:

$$A=\left[\begin{array}{rr}1&2\\\ a&1\end{array}\right]$$

...has two distinct, real, positive eigenvalues.

A

$0< a <\cfrac{1}{2}$.

B

$0\le a\le \cfrac{1}{2}$.

C

$|a|<\cfrac{1}{2}$.

D

$a>0$.