We have, A,Care3×3matrices B×Dare3×1matrices AX=Bhas unique solution CX=Dhas infinite solution. Since, AX=B have a unique solution. ⇒rank(A)=number of unknowns=3 ∴‌‌rank([A:B])=rank(A)=3...(i) Since, CX=D have infinite many solutions ∴‌Rank(C)=‌ not unique ‌⇒rank(C)<3 ⇒Rank([C:D])<3‌‌...(ii) From Eqs. (i) and (ii), we have Rank([A:D])≥rank[(C:B)]