Match the differential equations and their matrix function solutions:
It's good practice to multiply at least one matrix solution out fully, to make sure that you know how to do it, but you can get the other answers quickly by process of elimination and just multiply out one row or one column.

 1.

$y'(t)=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ -32 49 -23 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ -64 78 -34 64 -78 34

$y(t)$

 2.

$y'(t)=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ -86 218 -160 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 73 -49 80 111 -138 165

$y(t)$

 3.

$y'(t)=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 14 0 -4 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 2 13 -8 -3 0 25

$y(t)$

A.

$y(t)=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $0$ $-e^{26t}$ $4e^{13t}$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $-4e^{13t}$ $-2e^{26t}$ $5e^{13t}$ $0$ $3e^{26t}$ $e^{13t}$

B.

$y(t)=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $e^{60t}$ $-2e^{45t}$ $4e^{-75t}$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $-3e^{60t}$ $e^{45t}$ $-2e^{-75t}$ $-5e^{60t}$ $3e^{45t}$ $-3e^{-75t}$

C.

$y(t)=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $-1$ $3e^{64t}$ $-3e^{16t}$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $-3$ $4e^{64t}$ $-2e^{16t}$ $-5$ $-4e^{64t}$ $2e^{16t}$