TG EAMCET 2 May 2025 Shift 2 Paper

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)]