(Solved): Suppose A is a 22 real matrix with an eigenvalue =4+5i and corresponding eigenvector v=[1+ii ...

Suppose $A$ is a $2\times 2$ real matrix with an eigenvalue $?=4+5i$ and corresponding eigenvector $\vec{v}=\left[\begin{array}{c}?1+i\\ i\end{array}\right]\text{. }$ Determine a fundamental set (i.e, linearly independent set) of solutions for ${\vec{y}}^{?}=A\vec{y}$, where the fundamental set consists entirely of real solutions: Enter your solutions below, Use $t$ as the independent variable in your answers. $\begin{array}{l}{\vec{y}}_1(t)=[\\ {\vec{y}}_2(t)=[\end{array}]$