Consider the initial value problem

1. Find the eigenvalue $\lambda$, an eigenvector $\boldsymbol{\vec{v}_1}$, and a generalized eigenvector $\boldsymbol{\vec{v}_2}$ for the coefficient matrix of this linear system.
$\lambda =$ , $\boldsymbol{\vec{v}_1} =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$
, $\boldsymbol{\vec{v}_2} =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

2. Find the most general real-valued solution to the linear system of differential equations. Use $t$ as the independent variable in your answers.
$\boldsymbol{\vec{y}}(t) = c_1$
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$+ \ c_2$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

3. Solve the original initial value problem.
$y_1(t) =$
$y_2(t) =$