The general solution of the linear system $\boldsymbol{\vec{y}^{\,\prime}} = A \boldsymbol{\vec{y}}$ is

$$\boldsymbol{\vec{y}}(t) = \left\lbrack \begin{array}{rcl} e^{t/3} & 0 \\ 0 & e^{t/5} \end{array} \right\rbrack \left\lbrack \begin{array}{c} c_1 \\ c_2 \end{array} \right\rbrack.$$
Determine the constant coefficient matrix $A$.

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