My book with answers to proakis and manolakis book says that $F(x,n)=x(n)u(n)$ is time invariant while my calculation shows that it is time variant. I have repeated them many times and I am mostly convinced that book is wrong. Can somebody please check my calculations?
let $u(n)$ be a Heavside step function. First we shift output signal:
Let $x'(n)=x(n-k)$ be a shifted input signal. Lets calculate response to shifted input signal:
since $F(x, n - k) \neq F(x', n)$ this system is time variant. Is my method correct?