Find the explicit formula for the solution to the following linear iterative systems:
(a) $u^{(k+1)}=u^{(k)}-2 v^{(k)}, v^{(k+1)}=-2 u^{(k)}+v^{(k)}, u^{(0)}=1, v^{(0)}=0$.
(b) $u^{(k+1)}=u^{(k)}-\frac{2}{3} v^{(k)}, v^{(k+1)}=\frac{1}{2} u^{(k)}-\frac{1}{6} v^{(k)}, u^{(0)}=-2, v^{(0)}=3$.
(c) $u^{(k+1)}=u^{(k)}-v^{(k)}, v^{(k+1)}=-u^{(k)}+5 v^{(k)}, u^{(0)}=1, v^{(0)}=0$.
(d) $u^{(k+1)}=\frac{1}{2} u^{(k)}+v^{(k)}, v^{(k+1)}=v^{(k)}-2 w^{(k)}, w^{(k+1)}=\frac{1}{3} w^{(k)}$,
$$
u^{(0)}=1, v^{(0)}=-1, w^{(0)}=1 .
$$
$(e) u^{(k+1)}=-u^{(k)}+2 v^{(k)}-w^{(k)}, v^{(k+1)}=-6 u^{(k)}+7 v^{(k)}-4 w^{(k)}+$ $w^{(k+1)}=-6 u^{(k)}+6 v^{(k)}-4 w^{(k)}, \quad u^{(0)}=0, \quad v^{(0)}=1, \quad w^{(0)}=3$.