  The first direct, model-independent measurement is presented of the modulus
of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_\mathrm{tb}|$,
$|V_\mathrm{td}|$, and $|V_\mathrm{ts}|$, in final states enriched in single
top quark $t$-channel events. The analysis uses proton-proton collision data
from the LHC, collected during 2016 by the CMS experiment, at a centre-of-mass
energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$.
Processes directly sensitive to these matrix elements are considered at both
the production and decay vertices of the top quark. In the standard model
hypothesis of CKM unitarity, a lower limit of $|V_\mathrm{tb}|$ $>$ 0.970 is
measured at the 95% confidence level. Several theories beyond the standard
model are considered, and by releasing all constraints among the involved
parameters, the values $|V_\mathrm{tb}| =$ 0.988 $\pm$ 0.024, and
$|V_\mathrm{td}|^2 + |V_\mathrm{ts}|^2 =$ 0.06 $\pm$ 0.06, where the
uncertainties include both statistical and systematic components, are measured.
