  Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat
multiscale equations that contain a stiff part and a non-stiff part, where the
stiff part is characterized by a small parameter $\varepsilon$. In this work,
we prove rigorously the uniform stability and uniform accuracy of a class of
IMEX-RK schemes for a linear hyperbolic system with stiff relaxation. The
result we obtain is optimal in the sense that it holds regardless of the value
of $\varepsilon$ and the order of accuracy is the same as the design order of
the original scheme, i.e., there is no order reduction.
