Given the following matrix A

A $=$

$$

$$

$$

$$

$$

$3200$

$0400$

$0054$

$0022$

$$

$$

$$

$$

$$

$$

$($a$)$ Find all the eigenvalues.

$($b$)$ In MATLAB, if we do $,$ the output is given as follows

val $=$

$$

$$

$$

$$

$$

$6000$

$0$a $00$

$00$ a $0$

$0004$

$$

$$

$$

$$

$$

$,$ vec $=$

$$

$$

$$

$$

$$

$00$ c$10\mathrm{.}2747$

$00$ c$20\mathrm{.}9615$

$0\mathrm{.}97010\mathrm{.}4472$ c$30$

$0\mathrm{.}24250\mathrm{.}8944$ c$40$

$$

$$

$$

$$

$$

$.$

Find the eigenvectors of A corresponding to a and $$a$.$ Name the free variables

as t$1,$ t$2,$ so on so forth.

$($c$)$ Based on the result of pat $($b$),$ find the value of a and the vector c $=[$c$1$ c$2$ c$3$ c$4]$

T