Given L(x,y,z) = (0,0)

Is it a linear transformation?

Given L

( [x] )

[y] = [x+1] Is it a linear transformation? (The whole x y z matrix is equal to the x+1 y-z matrix)

[z] [y-z]

I am not real sure of the steps involved in determining if it is a linear transformation or not. Thanks for any help!