proof of this

3.3 Properties of Z-Transform 1. Linearity property The linearity property of Z-transform states that the Z-transform of linear weighted combination of discrete time signals is equal to similar linear weighted combination of Z-transform of individual discrete time signals. Let, Z{x,(n)} =X, (2) and Z{x_(n)} =X,(z) then by linearity property, Z{a,x,(n) +a,x,(n)} =a,X, (z)+a, X,(z) ; where, a, and a are constants