Suppose $A$ is a $2 \times 2$ real matrix with an eigenvalue $\lambda = 2 + 4 i$ and corresponding eigenvector

Determine a fundamental set (i.e., linearly independent set) of solutions for $\boldsymbol{\vec{y}^{\,\prime}} = A \boldsymbol{\vec{y}}$, where the fundamental set consists entirely of real solutions.

Enter your solutions below. Use $t$ as the independent variable in your answers.

$\boldsymbol{\vec{y}_1}(t) =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

$\boldsymbol{\vec{y}_2}(t) =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$