According to the formal definition, a transformation (also known as a function) y(t) = T(x(t)) is linear if and only if T(ax₁

Question

According to the formal definition, a transformation (also known as a
function) y(t) = T(x(t)) is linear if and only if
T(ax₁ (t) + bx₂(t)) = aT (x₁(t))+ bT(x₂(t)) = ay₁ (t) + by₂(t)
and is time-invariant if and only if for Vr 20
T(x(t-1)) = y(t-t)
Using this definition, evaluate if the following functions are linear or not:
1. T(x) = e-tx(t)
2. T(x)= x(t) dx(t)
dt
dx(t)
3. T(x)= t- dt
[6 marks

Kunduz · Accepted Answer

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