Obtain the matrix exponentials for the state matrices using four different approaches $($directly inverting

the resolvent matrix, Leverrier algorithm, Sylvester$$s expansion, and eigenstructure methods$)$:

a$)$ A $=$ diag$\{3,5,7\}$

b$)$ A $=$

$$

$001$

$010$

$600$

$$

$$

c$)$ A $=$

$$

$011$

$001$

$065$

$$

$$