Consider the linear system $\boldsymbol{\vec{y}^{\,\prime}} = A \boldsymbol{\vec{y}}$, where $A$ is a real $2 \times 2$ constant matrix with repeated eigenvalues. Use the given information to determine the matrix $A$.

Phase plane solution trajectories have horizontal tangents on the line $y_2 = 2 y_1$ and vertical tangents on the line $y_1 = 0$. The matrix $A$ has a nonzero repeated eigenvalue and $a_{21} = -3$.

$A =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$