onsider the LTI system

$$x $=$

$11$

$11$

x $+$

$1$

$0$

u

y $=11$ x $+2$u

$($i$)$ Determine the response of the system $($i$.$e$.,$ y$($t$))$ to zero input from initial condition x$0=$

$1$

$1$

$.$

$(3$ points$)$

$($ii$)$ Determine the response of the system to u$($t$)=$ cos$(5$t$)$ from zero initial condition. $(3$ points$)$

$($iii$)$ Determine the response of the system to u$($t$)=3$ cos$(5$t$)$ from initial condition x$0=$

$2$

$2$

$.$

$(2$ points$)$

Hint: You can use the formula

Z t

$0$

e cos$($ $)$d $=$ et cos$($t$)+$ sin$($t$)$

$2+$ $2$