consider continous time system yt xt2 where xt is the syste

consider continous time system y(t) = x(t-2) where x(t) is the system input and y(t) is the system output. Is system time invariant . Is system linear

Solution

y(t)=x(t-2);

For input x₁(t)

y₁(t)=x₁(t-2)

For input x₂(t)

y₂(t)=x₂(t-2)

For input x₃(t) =a*x₁(t)+b*x₂(t)

y₃(t)=a*x₁(t-2)+b*x₂(t-2)

y₃(t)=a*y₁(t)+b*y₂(t)

For Linear combination of inputs ,output is linear combination of its individual outputs

So system is Linear

For input x₁(t)

y₁(t)=x₁(t-2)

For input x₂(t) =x₁(t-t₀)

y₂(t)=x₁(t-t₀-2)=y₁(t-t₀)

Hence the system is Time Invariant