Exercise 7.  Prove the following properties of z-transforms.

7 (a).  Linearity:    .

Solution 7 (a).

See text and/or instructor's solution manual.

Given that      is valid for   ,  

and that      is valid for   .  

Hence

                      

Therefore,

                    

is valid for .  

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell