A system is defined with its input$/$output characteristic as; y$($t$)=$ x$($t$)+$ t$.$x$($t$-1)$ Discuss the following system properties for this system.

a$)(5$ pts$)$ Has this system memory?

b$)(5$ pts$)$ Is this system causal?

c$)(5$ pts$)$ Is this system BIBO stable?

d$)(5$ pts$)$ Is this system linear?

e$)(5$ pts$)$ Is this system time$-$invariant?