This is the first part of a four-part problem.

Let

1. Show that $\boldsymbol{\vec{y}_1}(t)$ is a solution to the system $\boldsymbol{\vec{y}^{\,\prime}} = P \boldsymbol{\vec{y}}$ by evaluating derivatives and the matrix product

Enter your answers in terms of the variable $t$.

 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$
=
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

2. Show that $\boldsymbol{\vec{y}_2}(t)$ is a solution to the system $\boldsymbol{\vec{y}^{\,\prime}} = P \boldsymbol{\vec{y}}$ by evaluating derivatives and the matrix product

Enter your answers in terms of the variable $t$.

 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$
=
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$