# Decomposing $SU(4)$ into $SU(3) \times U(1)$

I'm solving these problems concerning the $$SU(4)$$ group and I've reached the point where I have determined the Cartan matrix of $$SU(4)$$, its inverse and the weight schemes for $$(1 0 0)$$ and $$(0 1 0)$$ highest weight states.

How do I decompose the $$(1 0 0)$$ and $$(0 1 0)$$ into irreps of $$SU(3) \times U(1)$$ using the inverse of the Cartan matrix of $$SU(4)$$ and the weight scheme?