Problem$-2(25$ pts$)$: Given the following block diagram representation of a discrete$-$time system;

a$.$ Obtain the input$-$output relation $($differencel equation$)$ describing the system.$(4$pts$)$

b$.$ Let $a=1,b=2,c=\frac{3}{4},$ then find the zero$-$input response for $n0$ with the initial conditions of $y[0],y[-1]=1?(6$ pts $).$

c$.$ Find the zero$-$state response when the input $x[n]=Au[n].(6$ pts$).$

d$.$ Explain$/$show that whether this system is

i$.$ Stable or unstable? $(2$pts$)$

ii$.$ With or without memory? $(2$pts$)$

iii. Causal or anti$-$causal? $(2$ pts$)$

e$.$ Explain$/$show that this system is invertible or non$-$invertable? If invertible, find and draw the invers system yielding $x[n]$ from $y[n].(3$pts$)$