Project ForgeEngineering Mathematics
Linear Algebra
GATE 2009
Easy
The system of linear equations Ax=0, where A is an n×n matrix, has a non-trivial solution ONLY if
- Arank of A > n
- Brank of A = n
- rank of A < n
- DA is an identity matrix
Explanation
A homogeneous system Ax=0 has a non-trivial (nonzero) solution if and only if A is not full rank, i.e. rank(A)<n.
Source: GATE CH 2009 (2009)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.