Question

In the homogeneous system $\rho \left(A\right)<$ the number of unknowns then the system has

• A. Only trivial solution
• B. Trivial solution and infinitely many non-trivial solutions
• C. Only non-trivial solutions
• D. No solution

Answer 1

Answer: (B)

Trivial solution and infinitely many non-trivial solutions

Since the system of equations is consistent and it is a homogeneous equation, hence trivial solution exists.

Since $\rho \left(A\right)<$ number of unknowns, there are infinitely many non-trivial solutions to this system of equations.